The wavelengths of the spectral lines in the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The Rydberg constant $R$ for an atom is given by $R = \frac{\mu e^{4}}{8 \epsilon_{0}^{2} h^{3} c}$,where $\mu$ is the reduced mass of the electro

Vedclass · Accepted Answer

The mass of the two nuclei is different.

Vedclass · Answer

(C) The Rydberg constant $R$ for an atom is given by $R = \frac{\mu e^{4}}{8 \epsilon_{0}^{2} h^{3} c}$,where $\mu$ is the reduced mass of the electron-nucleus system. The reduced mass $\mu$ is defined as $\mu = \frac{m_{e} M}{m_{e} + M}$,where $m_{e}$ is the mass of the electron and $M$ is the mass of the nucleus. Since the mass of the deuterium nucleus $(M_{D} \approx 2M_{H})$ is different from the mass of the hydrogen nucleus $(M_{H})$,the reduced mass $\mu$ for deuterium is different from that of hydrogen. Consequently,the Rydberg constant $R$ and the resulting wavelengths of the spectral lines $(\frac{1}{\lambda} = R Z^{2} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}))$ differ slightly between the two.

The wavelengths of the spectral lines in the spectrum of deuterium $(_{1}H^{2})$ differ slightly from those in the spectrum of hydrogen $(_{1}H^{1})$ because ...

Similar Questions

The time period of revolution of an electron in the $n^{\text{th}}$ orbit in a hydrogen-like atom is given by $T = \frac{T_0 n^a}{Z^b}$,where $Z$ is the atomic number. Identify the correct values for $T_0$,$a$,and $b$.

The angular momentum of an electron in the hydrogen atom is $\frac{3h}{2\pi}$. Here $h$ is Planck's constant. The kinetic energy of this electron is.....$eV$

The figure shows standing de-Broglie waves due to the revolution of an electron in a certain orbit of a hydrogen atom. Then,the expression for the orbit radius is (All notations have their usual meanings).

Vedclass Test Series

Exam Paper Generator

Online Exam Module