Suppose an alpha particle accelerated by a potential of V volt is allowed to collide with a nucleus of atomic number Z, then the distance of closest approach of alpha particle to the nucleus is _____.

(a)

\(14.4\frac { Z }{ V } \mathring { A } \)

(b)

\(14.4\frac { V }{ Z } \mathring { A } \)

(c)

\(1.44\frac { Z }{ V } \mathring { A } \)

(d)

\(1.44\frac { V }{ Z } \mathring { A } \)

In a hydrogen atom, the electron revolving in the fourth orbit, has angular momentum equal to _____.

(a)

h

(b)

\(\frac{h}{\pi}\)

(c)

\(\frac{4h}{\pi}\)

(d)

\(\frac{2h}{\pi}\)

Atomic number of H-like atom with ionization potential 122.4 V for n = 1 is _____.

(a)

1

(b)

2

(c)

3

(d)

4

The ratio between the radius of first three orbits of hydrogen atom is _____.

(a)

1:2:3

(b)

2:4:6

(c)

1:4:9

(d)

1:3:5

The charge of cathode rays particle is _____.

(a)

Positive

(b)

negative

(c)

neutral

(d)

not defined

In J.J. Thomson e/m experiment, electrons are accelerated through 2.6 kV enter the region of crossed electric field and magnetic field of strength 3.0 x 10⁴ Vm^-1 and 1.0 x 10^-3 T, respectively, and pass through it and undeflected, then the specific charge is _____.

(a)

1.6 × 10¹⁰ C kg^–1

(b)

1.7 × 10¹¹ Ckg^–1

(c)

1.5 × 10¹¹ Ckg^–1

(d)

1.8 × 10¹¹ Ckg^–1

The ratio of the wavelengths radiation emitted for the transition from n = 2 to n = 1 in Li⁺⁺, He⁺ and H is _____.

(a)

1:2:3

(b)

1:4:9

(c)

3:2:1

(d)

4:9:36

The electric potential of an electron is given by \(V={ V }_{ 0 } \ In\left( \frac { r }{ { r }_{ 0 } } \right) \), where r₀ is a constant. If Bohr atom model is valid, then variation of radius of n^th orbit r_n with the principal quantum number n is _____.

(a)

\({ r }_{ n }∝ \frac { 1 }{ n } \)

(b)

\({ r }_{ n }∝ n\)

(c)

\({ r }_{ n }∝\frac { 1 }{ { n }^{ 2 } } \)

(d)

\({ r }_{ n }∝ { n }^{ 2 }\)

If the nuclear radius of ²⁷Al is 3.6 fermi, the approximate nuclear radius of ⁶⁴Cu, in femi is _____.

(a)

2:4

(b)

1.2

(c)

4.8

(d)

3.6

The nucleus is approximately spherical in shape. Then the surface area of nucleus having mass number A varies as _____.

(a)

A^2/3

(b)

A^4/3

(c)

A^1/3

(d)

A^5/3

The mass of a ₃⁷Li nucleus is 0.042 u less than the sum of the masses of all its nucleons. The binding energy per nucleon of ₃⁷Li nucleus is nearly _____.

(a)

46 MeV

(b)

5.6 MeV

(c)

3.9 MeV

(d)

23 MeV

M_p denotes the mass of the proton and M_n denotes mass of a neutron. A given nucleus of binding energy B, contains Z protons and N neutrons. The mass M(N, Z) of the nucleus is given by _____.(where c is the speed of light)

(a)

M (N,Z) = NM_n + ZM_p - Bc²

(b)

M (N,Z) = NM_n + ZM_p + Bc²

(c)

M (N,Z) = NM_n + ZM_p - B/c²

(d)

M (N,Z) = NM_n + ZM_p + B/c²

A radioactive nucleus (initial mass number A and atomic number Z) emits two α-particles and 2 positons. The ratio of number of neutrons to that of proton in the final nucleus will be _____.

(a)

\(\frac{A-Z-4}{Z-2}\)

(b)

\(\frac{A-Z-2}{Z-6}\)

(c)

\(\frac{A-Z-4}{Z-6}\)

(d)

\(\frac{A-Z-12}{Z-4}\)

The half-life period of a radioactive element A is same as the mean life time of another radioactive element B. Initially both have the same number of atoms. Then _____.

(a)

A and B have the same decay rate initially

(b)

A and B decay at the same rate always

(c)

B will decay at faster rate than A

(d)

A will decay at faster rate than B

A radiative element has N₀ number of nuclei at t = 0. The number of nuclei remaining after half of a half-life _____.(that is, at time t = \(\frac{1}{2}T_\frac{1}{2}\))

(a)

\(\frac{N_0}{2}\)

(b)

\(\frac{N_0}{\sqrt2}\)

(c)

\(\frac{N_0}{4}\)

(d)

\(\frac{N_0}{8}\)