Modern Physics Test

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Modern Physics Test - 4

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Question 1
4 / -1

A radioactive sample consists of two distinct species having equal number of atoms initially. The mean life time of one species is τ and that of the other is 5τ. The decay products in both cases are stable. A plot is made of the total number of radioactive nuclei as a function of time. Which of the following figures best represent the form of this plot?

A

B

C

D

Solution

....(i)
Adding (i) and (ii) we get
N = N₁ + N₂ = N₀ (e ^-t/τ+e^-t/5τ)
(a) is NOT the correct option as there is a time τ for which N is constant which means for time τ there is no process of radioactivity which does not makes sense. (b) and (c) shows intermediate increase in the number of radioactive atom which is IMPOSSIBLE as N will only decrease exponentially.
Question 2
4 / -1

The potential difference applied to an X-ray tube is 5kV and the current through it is 3.2mA. Then the number of electrons striking the target per second is

A
2 × 10¹⁶

B
5 × 10⁶

C
1 × 10¹⁷

D
4 × 10¹⁵

Solution

KEY CONCEPT :
No. of electrons striking the target per second
Question 3
4 / -1

A Hydrogen atom and a Li⁺⁺ion are both in the second excited state. If ℓ _H and ℓ _Li are their respective electronic angular momenta, and E_H and E_Li their respective energies, then

A

B

C

D

Solution
Question 4
4 / -1

The half-life of ²¹⁵At is 100 μ s. The time taken for the radioactivity of a sample of ²¹⁵At to decay to 1/16^th of its initial value is

A
400 μ s

B
6.3 μ s

C
40 μ s

D
300 μ s

Solution

A = A₀ (1/2)ⁿ; n = number of half lives.
Question 5
4 / -1

Which of the following processes represents a γ -decay ?

A

B

C

D

Solution

In γ-decay, the atomic number and mass number do not change.
Question 6
4 / -1

The electric potential between a proton and an electron is given by where r₀ is a constant. AssumingBohr’s model to be applicable, write variation of r_n with n, n being the principal quantum number?

A
r_n ∝ n

B
r_n ∝ 1/n

C
r_n ∝ n²

D
r_n ∝ 1/n²

Solution

Given potential energy between electron and proton
But this force acts as centripetal force
By Bohr’s postulate, mvr = nh/2π ...(ii)
From (i) and (ii),
Question 7
4 / -1

If the atom ₁₀₀Fm²⁵⁷ follows the Bohr model and the radius of ₁₀₀Fm²⁵⁷ is n times the Bohr radius, then find n.

A
100

B
200

C
4

D
1/4

Solution

KEY CONCEPT : For an atom followig Bohr ’s model, the radius is given by
= Bohr’s radius and m = orbit number.
For Fm, m = 5 (Fifth orbit in which the outermost electron is present)
Question 8
4 / -1

For uranium nucleus how does its mass vary with volume?

A
m ∝ V

B
m ∝ 1/V

C
m ∝ √V

D
m ∝ V²

Solution

KEY CONCEPT : We know that radius of the nucleus R = R₀A^1/3, where A is the mass number.
Volume ∝ mass.
Question 9
4 / -1

A nucleus with mass number 220 initially at rest emits an α -particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the α -particle

A
4.4 MeV

B
5.4 MeV

C
5.6 MeV

D
6.5 MeV

Solution

By conservation of momentum, p₁ = p₂
Solve equation (i) and (ii)
Question 10
4 / -1

In a photoelectric experiment anode potential is plotted against plate current.

A
A an d B will have different intensities while B an d C will have different frequencies

B
B an d C will ha ve different intensities while A an d C will have different frequencies

C
A an d B will have different intensities while A an d C will have equal frequencies

D
B and C will have equal intensities while A and B will have same frequencies

Solution

From the graph it is clear that A and B have the same stopping potential and therefore, the same frequency.
Also, B and C have the same intensity.