SP025 Brain Power Physics - Perak Matriculation College

TABLE OF CONTENTS 1
5
1.0 ELECTROSTATICS 5
2.0 CAPACITOR AND DIELECTRICS 12
3.0 ELECTRIC CURRENT AND DIRECT CURRENT CIRCUITS 16
4.0 MAGNETISM 18
5.0 ELECTROMAGNETIC INDUCTION 21
6.0 ALTERNATING CURRENT 23
7.0 GEOMETRICAL OPTICS 25
8.0 PHYSICAL OPTICS 26
9.0 QUANTIZATION OF LIGHT 26
10.0 WAVE PROPERTIES OF PARTICLE
11.0 NUCLEAR AND PARTICLE PHYSICS

2021 SP025 BRAIN POWER

Chapter 1: Electrostatics Week 1

Answer all questions.

1. (a)

Q2=+4.00 nC 3 cm Q1= +5.00 nC

4 cm

Q3=-6.00 nC

FIGURE 1-1
Three charges, Q1= +4.00 nC, charge Q2= +5.00 nC and Q3= -6.00 nC are arranged as in
FIGURE 1-1. Determine the magnitude of force acted on Q2.
(b)

q1=+3.5 C

0.5 m 0.5 m

q2=+1.0 0.5 m q3=–2.0 C
C FIGURE 1-2

Three point charges are located at the corners of an equilateral triangle with sides 0.5 m
as shown in FIGURE 1-2.

(i) Sketch the two forces that act on the +3.5 C charge.
(ii) Calculate the magnitude of each force.
(iii) Determine the magnitude and direction of the resultant force on

the +3.5 C charge.

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2. (a)

10 cm •P
10 cm

QA = +2 C QB = –8 C
FIGURE 1-3

FIGURE 1-3 shows the position of a point P with respect to two point charges, QA and
QB.

(i) Sketch and label the direction of the electric field strength by each point charge
at point P.

(ii) Determine the magnitude and direction of the electric
field strength at point P.

(b) Q₂
Q1

10 cm

FIGURE 1-4

FIGURE 1-4 shows two points charges Q1 = -2 µC and Q2 = -10 µC. At what distance
from charge Q1 between the charges where the net electric field is zero?

ANSWERS:

1. (a) 2.62 × 10−4 N
(b) (ii) 0.126N, 0.252 N
(iii) 0.218 N, 30° below positive x − axis

2. (a) (ii) 7.42 × 106 N C−1, 31° below positive x − axis
(b) 3.09 cm

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2021 SP025 BRAIN POWER

Chapter 1: Electrostatics Week 2
Answer all questions.

1. (a) 10 cm Q
+q
L 3 cm M 2 cm P
–q

FIGURE 1-5

FIGURE 1-5 shows two point charges, –q and +q fixed at point L and Q separated by a
distance of 15 cm. Given q = 5 C, calculate

(i) the electric potential at M and P.
(ii) the work done to bring a charge of 1 C from M to P.
(iii) the electric potential energy of the system when the 1 C charge is fixed at P.

(b)

q1 3.0 mm q3
+ +

4.0 mm

q2 - S
FIGURE 1-6

FIGURE 1-6 shows three point charges, q1 = 1.0x10-19 C, q2= -2.3x10-19 C and
q3=3.0x10-19 C. Calculate

(i) the electric potential at point S.
(ii) work needed to bring a proton of charge 1.6x10-19 C from infinity to point S.

2. (a)

RS +50 V
T +40 V

FIGURE 1-7 +30 V
+20 V
+10 V

0V

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FIGURE 1-7 shows the equipotential surfaces in a uniform electric field E of a parallel
plate. Calculate

(i) the work done by the electric field on a 5 C test charge that is displaced
from R to S and R to T.

(ii) the magnitude of electric field if the separation between the plates is 2 cm.
(b)

AB

12 mm
FIGURE 1-8
FIGURE 1-8 shows two parallel charged plates of equal magnitude and opposite sign.
The electric field between the plates is 5 x 104 N C−1. What is work done to displace a +
4 C charge from plate B to plate A?

ANSWERS:
1. (a) (i) – 450 x 103 V

(ii) 0.675 J
(iii) – 1.953 J
(b) (i) 1.65 x 10-7 V
(ii) – 2.64 x 10-26 J
2. (a) (i) – 1.5 x 10-4 J
(ii) 2500 V m-1
(b) 2.4 x 10-3 J

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Chapter 2: Capacitors and Dielectrics Week 3
Chapter 3: Electric Current and DC Current Week 3
Answer all questions.

1. Two capacitors of capacitance 2µF and 4µF, initially uncharged are connected in
series with a 12 V battery, calculate,
(a) the equivalent capacitance
(b) the charge on each capacitor
(c) the potential difference across each capacitor

2.
3 F 6 F

2 F 4 F

90V

FIGURE 2-1
For the system of capacitors shown in FIGURE 2-1, determine the
(a) charge on each capacitor.
(b) potential across each capacitor.
3.

FIGURE 2-2
In FIGURE 2-2, we charge a capacitor of capacitance C1 = 8 μF by connecting it to a
source of potential difference Vo = 120 V. The switch S is initially open. Once C1 is
charged, the source of potential difference is disconnected.
(a) (i) What is the charge Qo on C1 if switch S is left open?

(ii) What is the energy stored in C1 if switch S is left open?
(b) The capacitor of capacitance C2 = 4 μF is initially uncharged. After we close

switch S,
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2021 SP025 BRAIN POWER

(i) what is the potential difference across each capacitor and what is the
charge on each capacitor?

(ii) what is the total energy of the system after we close switch S?

4. A capacitor of 2.0 μF is charged using a 1.5 V battery. The charged capacitor is then
discharged through a 60 kΩ resistor.

(a) What is the time constant of the discharge circuit?
(b) Find the time taken for the charge on the capacitor to decrease to 1 .

e

5. A parallel plate capacitor is made up of two large parallel metal plates, each of area 200
cm2, and are 5.0 mm apart. The plates are charged to a potential difference of 20V.

(a) Calculate the
(i) capacitance of the capacitor
(ii) charge stored in the capacitor.

(b) The plates are now separated to a distance 10.0 mm with the supply still
connected.
(i) What is the charge stored in the capacitor?
(ii) If the supply is first disconnected before the plates are separated to a
distance of 10.0 mm, what is now the potential difference?

6. A capacitor has parallel plates of area 2000 cm2 separated by 1 cm apart. The capacitor
is connected to a power supply and charged to a potential difference Vo= 3000 V.

(a) Determine the
(i) capacitance Co.
(ii) magnitude of charge Q on each plate.

(b) It is then disconnected from the power supply and a sheet of insulating plastic
material is inserted between the plates, completely filling the space between
them. We find that the potential difference decreases to 1000 V while the charge
on each capacitor plate remains constant. Determine the

(i) capacitance C after the dielectric is inserted.
(ii) dielectric constant  r .

7. The current in a wire is 2.0 mA. In 2.0 ms,

(a) how much charge flows through a point in the wire
(b) how many electrons pass the point?

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2021 SP025 BRAIN POWER

8. A resistor made of a carbon rod has uniform cross-sectional area of 5.0 mm2. When a
potential difference of 15.0 V is applied across the ends of the rod, the rod carries a
current of 4.0 A. The resistivity of carbon is 3.5  10-5  m. Calculate the
(a) resistance of the rod.
(b) length of the rod.

9. A wire of cross-sectional area 0.8 mm2 is connected to a variable voltage, V and the
current, I in the wire is measured. At 27 C, the resistance of the wire is 0.25  and
the resistivity is 4.5  10-8  m. Calculate,

(a) the length of the wire.
(b) the change in the resistance of the wire when it is heated to 50 C.

(The temperature coefficient of resistivity of the wire is 3.9 10-3 C-1)

ANSWERS:

1. (a) 4/3 µF
(b) 16µC
(c) 8V, 4V

2. (a) 180 C,
(b) 120 C
(c) 60 V, 30V

3. (a) (i) 9.6 x 10-4 C
(ii) 0.058 J

(b) (i) 80 V, 640 C, 320 C
(ii) 0.038 J

4. (a) 0.12 s
(b) 0.12 s

5. (a) (i) 3.54 x 10-11 F,
(ii) 7.08 x 10-10 C

(b) (i) 3.54 x 10-10 C
(ii) 40 V

6. (a) (i) 1.77 x 10-10 F,
(ii) 5.31 x 10-7 C

(b) (i) 5.31 x 10-10 F
(ii) 3

7. (a) 4 µC
(b) 2.5 x 1013 electron

8. (a) 3.75 Ω
(b) 0.54 m

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2021 SP025 BRAIN POWER

9. (a) 4.44 m
(b) 0.0224 Ω

Chapter 3: Electric Current and Direct-Current Week 4
Answer all the questions.
1. A battery of emf 15.0 V has a terminal voltage of 11.6 V when connected to an external

load resistor R. If 12.5 W is delivered, calculate the
(a) resistance R.
(b) internal resistance of the battery.

2.

FIGURE 3-1

FIGURE 3-1 shows three resistors connected to a battery.

(a) Calculate the current drawn from the battery.
(b) Calculate the voltage across the 4  resistor.
(c) What is the current drawn from the battery if one of the 4  resistor is

removed?

R1= 2  I1 I3

3. ε2= 5 V

ε1= 10 V R2= 4  R3= 5 

I2

ε3= 8 V

FIGURE 3-2

Calculate the values of current I1, I2 and I3 in the circuit shown in FIGURE 3-2.

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2021 SP025 BRAIN POWER

ANSWERS:
1. (a) 13.92 Ω

(b) 4.08 Ω
2. (a) 1.2 A

(b) 2.4 V
(c) 0.86 A
3. I1 = 0.87 A
I2 = 0.82 A
I3 = –0.05 A

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2021 SP025 BRAIN POWER

Chapter 3: Electric Current and Direct-Current Week 5
Answer all the questions.
1. Power rating in a bulb is 150 W when it is connected to a 24 V supply.

(a) What is the resistance of the bulb?
(b) What is the current flow when it delivers only 80 W?

2. FIGURE 3-3 shows a voltage source is connected to two resistor

12 V R1= 8000 Ω

R2= 4000 Ω
Vout

FIGURE 3-3

(a) Calculate the output voltage.
(b) If the voltmeter resistance 4000 Ω is connected across the output, determine

the reading of the voltmeter.

3. A potentiometer is used to measure the emf of a thermocouple as shown in FIGURE
3-4. The driver cell has an emf of 2.0 V and its internal resistance is negligible. The
slide wire AB is 1.0 m long and of resistance 5.0 . When the galvanometer is balanced,
the length AJ is 65.5 cm. Calculate the emf of the thermocouple.

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2021 SP025 BRAIN POWER

FIGURE 3-4

ANSWERS:
1. (a) 3.84 A

(b) 4.56 A

2. (a) 4.0 V
(b) 2.4 V

3. 0.013 V

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2021 SP025 BRAIN POWER

Chapter 4: Magnetism Week 6

Answer all questions.

1. (a) (i) How to explain a magnetic field strength, B of a circular coil with radius, r
and carrying current, I is a straight line passing through the origin?

(ii) Sketch the magnetic field lines of the earth.

(b) A wire is bent and placed in a uniform magnetic field B. Current flows in the
wire as shown in FIGURE 4-1.

S

P B = 0.12 T 30 cm
3A 42

10 cm 20 cm R

Q

FIGURE 4-1

Determine the magnitude and direction of the force that acts on each segment PQ,
QR and RS.

(c) The length of a 500-turn solenoid is 3 cm. Calculate the magnetic field intensity
inside the solenoid when it carries a 0.6 A current.

(d) A particle with a charge of 4.8  10-19 C enters a uniform magnetic field with a
velocity of 2.0  105 m s-1 perpendicular to the field. Calculate the force that exerts
on the particle if the magnitude of the field is 1.5 T.

2. (a) (i) Sketch the magnetic field lines around a long current-carrying conductor.
(ii) Sketch the resultant magnetic field lines around two parallel long conductors
that carry currents in opposite directions.

(b) Two long parallel wires, P and Q are fixed on a horizontal plane in north-south
direction. Wire P is 10 cm left of Q. Wire P carries 40 A current northwards while
wire Q carries 20 A current southwards. Determine the magnitude and direction of

(i) the resultant magnetic field, B at midpoint between the wires.
(ii) the resultant magnetic field, B at a point on the horizontal plane, 8.0 cm from

wire P and 18 cm from wire Q from the right of the point.
(iii) the magnitude of the force per unit length, F/l on each wire.

(c) A 100-turn coil of mean cross-sectional area 15 cm2 carries 2.4 A current. Calculate
the maximum torque on the coil when it is placed in a 0.8 T magnetic field.

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2021 SP025 BRAIN POWER

ANSWERS:
1. (b) 0.036 N; 0 N; 0.08 N
(c) 0.013 N
(d) 1.44 x10-13 N
2. (b) (i) 2.4 x10-4 T
(ii) 7. x10-5 T
(iii) 1.6 x10-3 N m-1; 1.6 x10-3 N m-1
(c) 0.288 N m

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2021 SP025 BRAIN POWER

Chapter 4: Magnetism Week 7

Answer all questions.

1. (a) What will happen when two long parallel conductors which are free to move are
arranged 2 cm. A steady current of 10 A flows in each conductor in opposite
directions?

(b)

10.0cm

I1 = 5.0 A I2 = 8.0 A

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FIGURE 4-2
FIGURE 4-2 shows two long parallel current-carrying conductors separated by
10.0 cm. Determine the

(i) magnetic field created by wire 1 on wire 2.
(ii) force per unit length on wire 2 .

(c) A 20 turn circular coil has a diameter of 30.0 cm and carrying 2.00 A current placed
in a 1.5 T uniform magnetic field.

(i) Determine the maximum torque on the coil.
(ii) Does the maximum torque change if the circular coil is replaced with a square

coil having the same area, number of turns and current as the circular coil?
Explain your answer.

(d) In a velocity selector, a proton moves in a circle of radius 5.0 cm in a 0.60 T uniform
magnetic field, B. Determine the electric field, E such that the proton moves in a
straight path (undeflected).

2. (a) Sketch the magnetic field lines of a

(i) current-carrying straight wire.
(ii) current-carrying circular loop.

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2021 SP025 BRAIN POWER

(b)

8A

12 cm
5A

4 cm

FIGURE 4-3
FIGURE 4-3 shows a vertical straight wire inside a horizontal single loop. The radius,
r of the loop is 12 cm and the wire is 4 cm from the loop. The currents in the wire and
the loop are 8 A and 5 A respectively. Determine the magnitude and direction of the
resultant magnetic field at the centre of the loop.

(c) An electron is accelerated through a 100 V potential difference before
perpendicularly entering a uniform magnetic field. Inside the field, the electron
moves in circular trajectory of radius, r is 4 cm. Calculate the
(i) energy of the electron in joule.
(ii) centripetal force that acts on the electron.
(iii) magnitude of the magnetic field.

ANSWERS:
1. (b) (i) 1x10-5 T

(ii) 8 x10-5 N m-1
(c) (i) 4.24 Nm
(d) (i) 1.72 x106 N C-1
2. (b) 6.18 x10-6 T
(c) (i) 1.6 x10-17 J

(ii) 8.0 x10-16 N
(iii) 8.43 x10-4 T

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2021 SP025 BRAIN POWER

Chapter 5: Electromagnetic Induction Week 8
Answer all questions.

1. A 50-turn coil with cross-sectional area of 5.8  10-3 m2 is placed in a uniform magnetic
field of 1.5 T.

(a) Calculate the magnetic flux linkage in the coil when the plane of the coil makes
(b) an angle of 60 to the magnetic field.
The coil rotates about an axis perpendicular to the uniform magnetic field at a
2. constant angular velocity of 500 revolutions per second. What is the maximum
induced emf in the coil?

Q
v

P

FIGURE 5-1

FIGURE 5-1 shows a 30 cm rod PQ moving at velocity, v = 45 m s-1 across a uniform
magnetic field 0.8 T.
(a) Calculate the induced emf
(b) Determine the induced current and its direction if the resistance in the rod is 15

.
(c) Will emf be induced in the rod if it moves parallel to the magnetic field? Explain

your answer.

ANSWERS:
1. (a) 0.38 Wb

(b) 1366.59 V

2. (a) 10.8 V
(b) 0.72 A

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2021 SP025 BRAIN POWER

Chapter 5: Electromagnetic Induction Week 9
Answer all the questions

1. A steady current of 2 A in a coil of 400 turns causes a flux linkage of 10-4 Wb. Calculate
the
(a) inductance of the coil.
(b) average induced emf in the coil if the current reduces to zero in 0.08 s.
(c) energy stored in the coil.

2.

FIGURE 5-2
FIGURE 5-2 shows two solenoid P and Q placed near to each other.
(a) P and Q have 400 and 700 turns respectively. A current of 3.5 A flows in coil

P produces an average flux of 300 Wb through each turn of coil P and an
average flux of 90 Wb through each turn of coil Q. Calculate the mutual
inductance of the two solenoids.
(b) Explain why emf is induced in the coil Q when a sinusoidal voltage is connected
to the coil P, but no emf is induced if coil P is connected to a battery.
(c) Determine the direction of the induced current in the resistor R when terminal
X is positive and the current increases.

ANSWERS:
1. (a) 510−5 H

(b) 1.2510−3 V
(c) 110−4 J
2. (a) 0.018 H

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2021 SP025 BRAIN POWER

Chapter 6: Alternating Current Week 10
Answer all questions.
1. A capacitor, a coil and two resistors of equal resistance are arranged in an AC circuit,

as shown in FIGURE 6-1. An AC source provides an emf of 20 V (rms) at a frequency
of 60 Hz.
When the double-throw switch S is open, the rms current is 183 mA.
When the switch is closed in position 1, the rms current is 298 mA.
When the switch is closed in position 2, the rms current is 137 mA.
Calculate the value of R, C and L.

C

R R
L
20 V 1

S

60 Hz 2

FIGURE 6-1

2.
40 

50 mH ~

50 μF

FIGURE 6-2

The voltage source in FIGURE 6-2 has an rms output of 100 V at an angular frequency
of 1000 rad s-1.

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2021 SP025 BRAIN POWER

Calculate the
(a) rms current in the circuit
(b) power supplied by the source.
Show that the power delivered to the resistor is equal to the power supplied by the
source.
ANSWERS:
1. 99.6 Ω, 2.49 x 10-5 F, 0.164 or 0.402 H
2. (a) 2 A
(b) 160 W

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2021 SP025 BRAIN POWER

Chapter 6: Alternating Current Week 11
Answer all questions.
1.

200 μF 200 Ω

45 V (rms)

100 Ω 3 mH

FIGURE 6-3

In FIGURE 6-3, calculate the rms current delivered by 45 V (rms) power supply when

(a) the frequency is very large and
(b) the frequency is very small.

2. A series RLC circuit has a resistance of 45 Ω and an impedance of 75 Ω. Calculate
average power is delivered to the circuit when Vrms = 210 V.

ANSWERS:

1. (a) 225 mA
(b) 450 mA

2. 353 W

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2021 SP025 BRAIN POWER

Chapter 7: Geometrical Optics Week 12
Answer all questions.
1. A 1.8 m tall shopper in a department store is 5.8 m from a convex security mirror. The

shopper notices that his image in the mirror appears to be only 16.3 cm tall. Determine
radius of curvature of the mirror. Is the image upright or inverted? Sketch a ray diagram
to show the formation of image.
2. A vertical object is placed in front of a spherical mirror and the linear magnification of
the image is 3. If an upright image is formed 30.0 cm from the centre of the mirror:
(a) sketch a ray diagram to show the formation of the image,
(b) calculate the distance of the object from the pole of the mirror and
(c) calculate the focal length of the mirror.

ANSWERS:
1. - 1.2 m (virtual image)
2. (b) 10 cm

(c) 15 cm

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2021 SP025 BRAIN POWER

Chapter 7: Geometrical Optics Week 13

Answer all questions.

1. A goldfish is swimming in water (n = 1.33) inside a spherical plastic bowl of index of
refraction 1.33. If the goldfish is 10 cm from the front wall of the 15 cm radius bowl,

(a) Where does the goldfish appear to an observer in front of the bowl?
(b) The fishbowl is placed near the window where it will receive the evening sunlight.

Is there any risk that the eyes of the fish may be damaged because sunlight may
focus sharply on it? Explain.

2. A biconvex lens forms a virtual image of an object placed at a distance 5.0 cm from lens.
If the image formed is three times bigger than the object.

(a) Determine the position of the image.
(b) Calculate the focal length of the lens.
(c) Sketch a ray diagram to show the formation of image.

3. A contact lens has an outer convex surface of radius 5.0 cm and the inner concave surface
of radius 6.0 cm. The refractive index of the lens is 2.0.

(a) Determine the focal length of this lens.
(b) State whether the refracted ray from this lens is converged or diverged. Explain.

4. A plano-convex lens with radius of 12 cm is made with refractive index of 2.5.

(a) Sketch the shape of the lens.
(b) Determine the focal length of this lens.
(c) Determine the image distance from the lens if the real image formed is four times

than the real object.

ANSWERS:

1. (a) - 9 cm
(b) 60.45 cm (no risk)

2. (a) – 15 cm
(b) 7.5 cm

3. (a) 30 cm
(b) The refracted ray from this lens is converged because the focal length of the lens
is positive (converging lens)

4. (b) 7.5 cm
(c) 40 cm

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Chapter 8: Physical Optics Week 14
Answer all questions.

1. Coherent light with a wavelength of 475 nm is incident on a double slits and its
interference pattern is observed on a screen at 85 cm from the slits. The third
bright fringe occurs at 3.11 cm from the central maximum. Calculate
(i) the separation distance between slits.
(ii) the distance from the central maximum to the third dark fringe.

2. The walls of soap bubble have about the same index of refraction as that of plain
water, n = 1.33. There is air both inside and outside the bubble.
(i) What wavelength of visible light is most strongly reflected from a point
on a soap bubble where its wall is 290 nm thick.
(ii) To what color does this correspond.
(iii) Repeat part (i) for a wall thickness of 340 nm.
Given, violet = 400 − 450 nm, blue = 450 − 520 nm, green = 520 − 560 nm,
yellow = 560 − 600 nm

ANSWERS:
1. (i) 3.98 10−5 m

(ii) 0.026 m
2. (i) 514 nm

(ii) Blue
(iii) 603 nm

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Chapter 8: Physical Optics Week 15
Answer all questions.
1. A slit is illuminated with light of wavelength 650 nm and the first minimum appears at

10.
(i) Calculate the width of the slit.
(ii) The slit is illuminated with a light of different wavelength and the first

maximum appears at the same angle. What is the wavelength of the light used?

2. A 500 nm light is incident normally on a diffraction grating. The third-order maximum
of the diffraction pattern is observed at 32.
(i) Calculate the number of lines per cm of the grating.
(ii) How many bright fringes can be observed?

ANSWERS:
1. (i) 3.74 10−6 m

(ii) 433 nm
2. (i) 3533 lines per cm

(ii) 11

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Chapter 9: Quantization Of Light Week 16
Answer all questions.
[ = 3.00 × 108 −1, ℎ = 6.63 × 10−34 , = 9.11 × 10−31 ,
= 1.6 × 10−19 ]
1. In a photoelectric effect experiment, a beam of light of wavelength 400 nm is incident on

a sodium surface. The work function of sodium is 2.28 eV. Calculate
(a) the threshold wavelength of sodium.
(b) the maximum kinetic energy of photoelectrons.
(c) the stopping potential of the photoelectrons.
(d) the maximum velocity of ejected photoelectrons.

2. A photocell detects light by means of the photoelectric effect. You are given a cesium
photocell with work function 2.1 eV and an aluminium photocell with work function 4.3
eV.
(a) What is the threshold frequency of the cesium and aluminium photocells?
(b) Calculate the maximum speed of the emitted electron in the cesium photocell if
a 250 nm light is shone on it.

3. A 424 nm light incidences on a metal of a work function of 2.28 eV.
(a) Calculate the stopping potential.
(b) What is the maximum speed of the emitted electrons?

ANSWERS:
1. (a) 545.23
(b) 1.32 × 10−19
(c) 0.826
(d) 5.39 × 105 −1
2. (a) 5.068 × 1014 ,1.038 × 1015
(b) 1.004 × 106 −1
3. ( ) 0.65
(b) 4.78 × 105 −1

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Chapter 10: Wave Properties Of Particle Week 17
Chapter 11: Nuclear And Particle Physics Week 17

Answer all questions.
[ = 3.00 × 108 −1, ℎ = 6.63 × 10−34 , = 9.11 × 10−31 ,

= 1.6 × 10−19 ]

1. An electron is accelerated in vacuum through a potential difference of 1500 V. If
the potential difference is doubled, calculate

(a) the ratio of the electron's new speed to its original speed
(b) the new wavelength of the electron.
(c) the momentum and energy (in eV) of light of wavelength 680 nm.

2. In an electron diffraction experiment, a beam of electrons is directed towards a crystal

of inter atomic spacing of 0.345 nm. If the first order of the maximum intensity occurs
at an angle, θ = 47°, calculate the speed of the electron.

3. An electron of mass me and charge e is accelerated between two plates with
potential differences of V. If the voltage applied across the plate is 1 kV, calculate
the de Broglie wavelength of the electron.

[ = 1.007277 , = 1.008665 , = 5.48 × 10−4 ,
= 1.6 × 10−19 , 1 = 1.66 × 10−27 ]

4. Uranium isotope 23928 has atomic mass 238.050783 u. Calculate

(a) the number of proton, neutron and nucleon in the nucleus.
(b) the mass defect in atomic mass unit, u.
(c) the binding energy in MeV.
(d) the binding energy per nucleon.

5. The mass of gold nucleus 197 Au is 196.966569 u. Calculate the
79

(a) mass defect of the nucleus.
(b) binding energy per nucleon of the nucleus.

ANSWERS:

1. (b) 2.24 × 10−11

(c) 1.83 )
2. 4.33 × 106 −1
3. 3.88 × 10−11
4. (b) 1.934207

(c) 1801.71

(d) 7.57

5. (a) 1.630784
(b) 1.24 × 10−12 /

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2021 SP025 BRAIN POWER

Chapter 11: Nuclear And Particle Physics Week 18

Answer all questions.
1. The activity of a sample of radioisotope changes from 1500 Bq to 1300 Bq in 25 minutes.

Calculate the

(a) decay constant.
(b) half-life
(c) initial number of radioactive nuclei.
(d) number of radioactive nuclei decayed within 25 minutes.

2. A sample of radioisotope thorium-234 with a half-life of 24.5 days has an activity 6.1 
1014 decays per second. Calculate

(a) the decay constant.
(b) the mass of the sample.

3. The activity of a radioisotope sample is 12 mCi. After 5 hours, the activity is 9 mCi. Given
1Ci = 3.7  1010 Bq. Calculate the

(a) decay constant.
(b) half-life.
(c) initial number of nuclei in the sample.
(d) activity of the sample after 30 hours.

4. Carbon-14 with a half-life of 5730 years is used to date s bone found at an archaeological
excavation. If the ratio of 14C to 12C atoms of the bone is 3.25  10-13, how old is the bone?
The ratio of 14C to 12C atoms in living matter is 1.3  10-12.

ANSWERS:

1. (a) 9.54 × 10−5 −1
(b) 7265.69
(c) 1.57 × 107
(d) 1.36 × 107

2. (a) 3.27 × 10−7 −1
(b) 0.73

3. (a) 1.6 × 10−5 −1

(b) 43321.7

(c) 2.78 × 1013

(d) 7.89 × 107

4. = 11456.98

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