Atoms practice · Mixed difficulty

An electron revolving in $n^{\text {th}}$ Bohr orbit has magnetic moment $\mu_n.$ If $\mu_n \propto n^x,$ the value of $x$ is

${v_1}$ is the frequency of the series limit of Lyman series,${v_2}$ is the frequency of the first line of Lyman series and ${v_3}$ is the frequency of the series limit of the Balmer series. Then

A electron collides elastically with $H$-like atom and excites it from ground state to $n=3$. Find out the energy transfer to $H$-like atom.

An Electron is revolving around nucleus of charge Ze, if 40.8 eV of energy needed to excite an electron from n=1 to n=2 state. What is value of Z?

Energy of electron (in $\mathrm{eV}$) in $2^{\text {nd}}$ orbit of $He^+$ ion is

The significant result deduced from the
Rutherford's scattering experiment is that

The ratio of the wavelengths for $2 \to 1$ transition on $L{i^{ + + }},H{e^ + }$ and $H$ is

An $X$-rays tube is working at a potential difference of $38.08 \,\mathrm{kV}$. The potential difference is decreased to half its initial value. It is found that difference of the wavelength of $K_\alpha \,{X}$-ray and the most energetic continuous $X$-rays becomes 4 times of the difference prior to the change of voltage. Assuming $K_\alpha$ line is present in both cases, find the atomic number of the target element. [Take: $R c h=13.6 \,\mathrm{eV}$]

In the Bohr model of a $\pi$-mesic atom, a $\pi$-meson of mass $m_\pi$ and of the same change as the electron is in a circular orbit of radius $r$ about the nucleus with an orbital angular momentum $\frac{h}{2 \pi}$. If the radius of a nucleus of atomic number $Z$ is given by $R=1.6 \times 10^{-15} Z^{\frac{1}{3}} \mathrm{~m}$. The limit on $Z$ for which $\left(\frac{\varepsilon_0 h^2}{\pi m e^2}=0.53 \mathop A\limits^ \circ\right.$ and $\left.\frac{m_{\pi}}{m_e}=264\right) \pi$-mesic atoms might exist is:

Which of the relation is correct between time period and number of orbits while an electron is revolving in an orbit