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. $\frac{1}{\mathrm{m}}$