An electron is moving around the nucleus of a hydrogen atom in a circular orbit of radius r. What is the coulomb force $\overrightarrow{\mathrm{F}}$ between the two? \(\left ( \text{where},K=\frac{1}{4\pi \epsilon _{0}} \right )\)

1. $\mathrm{K}\frac{{\mathrm{e}}^2}{{\mathrm{r}}^2}\hat{\mathrm{r}}$

2. $-\mathrm{K}\frac{{\mathrm{e}}^2}{{\mathrm{r}}^3}\hat{\mathrm{r}}$

3. $\mathrm{K}\frac{{\mathrm{e}}^2}{{\mathrm{r}}^3}\overrightarrow{\mathrm{r}}$

4. $-\mathrm{K}\frac{{\mathrm{e}}^2}{{\mathrm{r}}^3}\overrightarrow{\mathrm{r}}$

When an electron transitions from n = 4 to n = 2, then the emitted line in the spectrum will be:

The total energy of an electron in the first excited state of a hydrogen atom is about –3.4 eV. Its kinetic energy in this state will be:

1. –6.8 eV

2. 3.4 eV

3. 6.8 eV

4. –3.4 eV

What was Rutherford's atom according to classical theory?

The radius of the first permitted Bohr orbit for the electron in a hydrogen atom equals $0.5$ $\stackrel{o}{A}$ and its ground state energy equals -13.6 eV. If the electron in the hydrogen atom is replaced by a muon (μ-) [ charged the same as the electron and mass 207 m_e], the first Bohr radius and ground state energy will be: 
(\(m_e\) represents mass of electron)

When an α– particle of mass m moving with velocity v bombards a heavy nucleus of charge Ze, its distance of closest approach from the nucleus depends on m as:

1. $\frac{1}{\sqrt{\mathrm{m}}}$

2. $\frac{1}{{\mathrm{m}}^2}$

3. m

4. $\frac{1}{\mathrm{m}}$

The ionisation potential of the hydrogen atom is 13.6 eV. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy of 12.1 eV. According to Bohr’s theory, the spectral lines emitted by hydrogen atoms will be:

1. two

2. three

3. four

4. one

The wavelength of the first line of Lyman series for hydrogen atom is equal to that of the second line of Balmer series for a hydrogen like ion. What is the atomic number Z of hydrogen like ion?

1. 4

2. 1

3. 2

4. 3

What is the ratio of wavelengths of the last line of the Balmer series and the last line of the Lyman series?

1. 1

2. 4

3. 0.5

4. 2

What happens when an electron makes a transition from an excited state to the ground state of a hydrogen-like atom or ion?