Modern Physics Test

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Modern Physics Test - 6

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Weekly Quiz Competition

Question 1
4 / -1

Which one of the following statements is WRONG in the context of X-rays generated from a X-ray tube?

A
Wavelength of characteristic X-rays decreases when the atomic number of the target increases.

B
Cut-off wavelength of the continuous X-rays depends on the atomic number of the target

C
Intensity of the characteristic X-rays depends on the electrical power given to the X-ray tube

D
Cut-off wavelength of the continuous X-rays depends on the energy of the electrons in the X-ray tube

Solution

The continuous spectrum depends on the accelerating voltage. It has a definite minimum wavelength.
Greater the accelerating voltage for electrons, higher will be the kinetic energy it attains before striking the target, higher will be the frequency of X - rays and smaller will be the wavelength. The wavelength of continuous X - rays is independent of the atomic number of target material.
Question 2
4 / -1

A radioactive sample S₁ having an activity 5_µCi has twice the number of nuclei as another sample S₂ which has an activity of 10 _µCi. The half lives of S₁ and S₂ can be

A
20 years and 5 years, respectively

B
20 years and 10 years, respectively

C
10 years each

D
5 years each

Solution
Question 3
4 / -1

Photoelectric effect experiments are performed using three different metal plates p, q and r having work functions φ_p = 2.0 eV, φ_q = 2.5 eV and φ_r = 3.0 eV, respectively. A light beam containing wavelengths of 550 nm, 450 nm and 350 nm with equal intensities illuminates each of the plates. The correct I-V graph for the experiment is [Take hc = 1240 eV nm]

A

B

C

D

Solution

The energy possessed by photons of wavelen gth 550 nm is 1240/550 = 2.25eV
The energy possessed by photons of wavelength 450 nm is 1240/450 = 2.76eV
The energy possessed by photons of wavelength 350 nm is 1240/350 = 3.5.eV
For metal plate p :
φ_p = 2 eV.
Photons of wavelength 550 nm will not be able to eject electrons and therefore, the current is smaller than p.
The work function is greater than q therefore the stopping potential is lower in comparison to p.
For metal plate r :
φ_r = 3 eV
Only wavelength of 350 nm will be able to eject electrons and therefore, current is minimum. Also the stopping potential is least.
Question 4
4 / -1

The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 A°. The wavelength of the second spectral line in the Balmer series of singly-ionized helium atom is

A
1215 A°

B
1640 A°

C
2430 A°

D
4687 A°

Solution

The wave length of first spectral line in the Balmer series of hydrogen atom is 6561Å . Here n₂ = 3 and n₁ = 2
For the second spectral line in the Balmer series of singly ionised helium ion n₂ = 4 and n₁ = 2 ; Z = 2
Dividing equation (i) and equation (ii) we get
Question 5
4 / -1

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3×10⁸ ms^–1. The final momentum of the object is

A
0.3 × 10^–17 kg ms^–1

B
3.0 × 10^–17 kg ms^–1

C
1.0 × 10^–17 kg ms^–1

D
9.0 × 10^–17 kg ms^–1

Solution
Question 6
4 / -1

If λ_Cu is the wavelength of K_α X-ray line of copper (atomic number 29) and λ_Mo is the wavelength of the K_α X-ray line of molybdenum (atomic number 42), then the ratio λ_Cu/λ_Mo is close to

A
1.99

B
2.14

C
0.50

D
0.48

Solution
Question 7
4 / -1

A metal surface is illuminat ed by light of two different wavelengths 248 nm and 310 nm. The maximum speeds of the photoelectrons corresponding to these wavelengths are u₁ and u₂, respectively. If the ratio u₁ : u₂ = 2 : 1 and h_c = 1240 eV nm, the work function of the metal is nearly

A
3.7 eV

B
3.2 eV

C
2.8 eV

D
2.5 eV

Solution

Dividing the above two equations, we get
Question 8
4 / -1

In a historical experiment to determine Planck's constant, a metal surface was irradiated with light of different wavelengths. The emitted photoelectron energies were measured by applying a stopping potential. The relevant data for the wavelength (λ) of incident light and the corresponding stopping potential (V₀) are given below :
Given that c = 3 × 10⁸m s^–1and e = 1.6 × 10^–19 C , Planck's constant (in units of J s) found from such an experiment is

A
6.0 × 10^–34

B
6.4 × 10^–34

C
6.6 × 10^–34

D
6.8 × 10^–34

Solution

From the first two values given in data
Similarly if we calculate h for the last two values of data h = 6.4 × 10^–34J-s
Question 9
4 / -1

The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of radius R is given by
The measured masses of the neutron are 1.008665 u, 1.007825 u, 15.000109 u and 15.003065 u, respectively. Given that the radii of both the nuclei are same, 1 u = 931.5 Me V/c² (c is the speed of light) and e²/(4 πε₀) = 1.44 MeV fm. Assuming that the difference between the binding energies of is purely due to the electrostatic energy, the radius of either of the nuclei is (1 fm = 10^–15 m)

A
2.85 fm

B
3.03 fm

C
3.42 fm

D
3.80 fm

Solution

Binding energy of nitrogen atom
= [8 × 1.008665 + 7 × 1.007825 – 15.000109] × 931
Binding energy of oxygen atom
= [7 × 1.008665 + 8 × 1.007825 – 15.003065] × 931
∴ Difference = 0.0037960 × 931 MeV ...(I)

From (i) & (ii)
Question 10
4 / -1

An accident in a nuclear labora tory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?

A
64

B
90

C
108

D
120

Solution