Modern Physics Test

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Modern Physics Test - 3

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Question 1
4 / -1

Order of magnitude of density of uranium nucleus is, [m_p = 1.67 × 10^–27kg]

A
10²⁰kg/m³

B
10¹⁷kg/m³

C
10¹⁴kg/m³

D
10¹¹kg/m³

Solution

Nuclear density of an atom of mass number A,
Question 2
4 / -1

²²Ne nucleus, after absorbing energy, decays into two aparticles and an unknown nucleus. The unknown nucleus is

A
nitrogen

B
carbon

C
bor on

D
oxygen

Solution

The new element X has atomic number 6. Therefore, it is carbon atom.
Question 3
4 / -1

Binding energy per nucleon vs mass number curve for nuclei is shown in the Figure. W, X, Y and Z are four nuclei indicated on the curve. The process that would release energy is

A
Y → 2Z

B
W → X+Z

C
W → 2Y

D
X → Y+Z

Solution

KEY CONCEPT : Energy is released when stability increases. This will happen when binding energy per nucleon increases.
Question 4
4 / -1

Imagine an atom made up of a proton and a hypothetical particle of double the mass of the electron but having the same charge as the electron. Apply the Bohr atom model and consider all possible transitions of this hypothetical particle to the first excited level. The longest wavelength photon that will be emitted has wavelength λ (given in terms of the Rydberg constant R for the hydrogen atom) equal to

A
9/(5R)

B
36/(5R)

C
18/(5R)

D
4/R

Solution

KEY CONCEPT :
For ordinary hydrogen atom, longest wavelength
With hypothetical particle, required wavelength
Question 5
4 / -1

The electron in a hydrogen atom makes a transition from an excited state to the ground state. Which of the following statements is true ?

A
Its kinetic energy increases and its potential and total energies decreases.

B
Its kinetic energy decreases, potential energy increases and its total energy remains the same.

C
Its kinetic and total energies decrease and its potential energy increases.

D
Its kinetic, potential and total energies decrease.

Solution

NOTE : As the electron comes nearer to the nucleus the potential energy decreases
Question 6
4 / -1

Two radioactive materials X₁ and X₂ have decay constants 10λ and λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X₁ to that of X₂ will be 1/e after a time

A
1/ 10λ

B
1/ 11λ

C
11/ 10λ

D
1/ 9λ

Solution
Question 7
4 / -1

Electrons with energy 80 keV are incident on the tungsten target of an X-ray tube. K-shell electrons of tungsten have 72.5 keV energy. X-rays emitted by the tube contain only

A
a continuous X-ray spectrum (Bremsstrahlung) with a minimum wavelength of 0.155Å

B
a continuous X-ray spectrum (Bremsstrahlung) with all wavelengths

C
the characteristic X-ray spectrum of tungsten

D
a continuous X-ray spectrum (Bremsstrahlung) with a minimum wavelength of 0.155Å and the characteristic X-ray spectrum of tungsten.

Solution

KEY CONCEPT :
Energy of incident electrons is greater than the ionization energy of electrons in K-shell, the K-shell electrons will be knocked off. Hence, characteristic X-ray spectrum will be obtained.
Question 8
4 / -1

The electron emitted in beta radiation originates from

A
inner orbits of atoms

B
free electrons existing in nuclei

C
decay of a neutron in a nucleus

D
photon escaping from the nucleus

Solution

Note : In a nucleus neutron converts into proton as follows n → p⁺ + e^–1 Thus, decay of neutron is responsible for b-radiation origination
Question 9
4 / -1

The transition from the state n = 4 to n = 3 in a hydrogen-like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition

A
2 → 1

B
3 → 2

C
4 → 2

D
5 → 4

Solution

For 2 to 1, 3 to 2 and 4 to 2 we get energy that n = 4 to n = 3,
I.R. radiation has less energy than U.V. radiation.
Question 10
4 / -1

The intensity of X-rays from a Coolidge tube is plotted against wavelength λ as shown in the figure. The minimum wavelength found is λ_C and the wavelength of the K_α line is λ_K. As the accelerating voltage is increased

A
λ_K - λ_C increases

B
λ_K - l_C decreases

C
λ_K increases

D
λ_K decreases

Solution

KEY CONCEPT :
In case of Coolidge tube
Thus the cut off wavelength is inversely proportional to accelerating voltage. As V increases, λ_c decreases. λ_k is the wavelength of K_∝ line which is a characteristic of an atom and does not depend on accelerating voltage of bombarding electron since λ_k always refers to a photon wavelength of transition of e^– from the target element from 2 → 1.
The above two facts lead to the conclusion that λ_k – λ_c increases as accelerating voltage is increased.