The energy of a hydrogen atom in its ground state is —13.6 eV. The energy of the level corresponding to the quantum number n = 2 (first excited state) in the hydrogen atom is:

1. -2.72 eV

2. - 0.85 eV

3. -0.54 eV

4. — 3.4 eV

 

Magnetic moment due to the motion of the electron in ${\mathrm{n}}^{\mathrm{th}}$  energy state of a hydrogen atom is proportional to

1.  n

2.  ${\mathrm{n}}^0$

3.  ${\mathrm{n}}^5$

4.  ${\mathrm{n}}^3$

When the electron of a hydrogen-like atom jumps from a higher energy level to a lower energy level, then,

1.  the angular momentum of the electron remains constant.

2.  the kinetic energy of the electron increases.

3.  the wavelength of the de-Broglie wave associated with the motion of the electron increases.

4.  the potential energy increases.

The frequency Of radiation emitted during the transition of an electron from a second excited state to a first excited state in H-atom is ${\mathrm{f}}_0.$ The frequency of the same transition emitted by a singly ionized He ion is

1.  $2{\mathrm{f}}_0$

2.  $4{\mathrm{f}}_0$

3.  $\frac{{\mathrm{f}}_0}{2}$

4.  $\frac{{\mathrm{f}}_0}{4}$

The longest and shortest wavelength of the Lyman series are (respectively)

1.  $1215 \stackrel{0}{\mathrm{A}}, 500 \stackrel{0}{\mathrm{A}}$

2.  $1215 \stackrel{0}{\mathrm{A}}, 912 \stackrel{0}{\mathrm{A}}$

3.  $912 \stackrel{0}{\mathrm{A}}, 500 \stackrel{0}{\mathrm{A}}$

4. $912 \stackrel{0}{\mathrm{A}}, 700 \stackrel{0}{\mathrm{A}}$

The ratio of wavelengths of the last line of Balmer series and the last line of Lyman series is: 

(1) 2

(2) 1

(3) 4

(4) 0.05

Given the value of Rydberg constant is ${10}^7 m^{-1}$, the wave number of the last line of the Balmer series in hydrogen spectrum will be:

(a) $0.5\times {10}^7{m}^{-1}$        (b) $0.25\times {10}^7{m}^{-1}$

(c) $2.5\times {10}^7{m}^{-1}$        (d) $0.025\times {10}^4{m}^{-1}$

Considering the \(3^{rd}\) orbit of \(\mathrm{He}^{+}\) (Helium ion), using the non-relativistic approach, the speed of the electron in this orbit will be: (Given: \(Z=2, K = 9\times 10^{9}\), and Planck's constant, \(h= 6.6\times10^{-34}\) J-s)
1. \(2.92\times 10^{8}\) m/s
2. \(1.46\times 10^{6}\) m/s
3. \(0.73\times 10^{8}\) m/s
4. \(3.0\times 10^{8}\) m/s

Electron in hydrogen atom first jumps from third exicted state to second exicted state and then from second exicted to the first excited state. The ratio of the wavelengths ${\lambda }_1:{\lambda }_2$ emitted in the two cases is

(1) 7/5

(2) 27/20

(3) 27/5

(4) 20/7