When an electron in a hydrogen atom jumps fro | vedclass

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

Question

(B) The de-Broglie wavelength is given by $\lambda = \frac{h}{p}$,where $h$ is Planck's constant and $p$ is the momentum of the electron. Since $p = m

Vedclass · Accepted Answer

$\frac{1}{4}$

Vedclass · Answer

(B) The de-Broglie wavelength is given by $\lambda = \frac{h}{p}$,where $h$ is Planck's constant and $p$ is the momentum of the electron. Since $p = mv$ and kinetic energy $E_K = \frac{p^2}{2m}$,we have $p = \sqrt{2mE_K}$. Thus,$\lambda = \frac{h}{\sqrt{2mE_K}}$. For an electron in a hydrogen atom,the velocity $v$ in the $n^{	ext{th}}$ orbit is given by $v_n = \frac{v_0 Z}{n}$. Since $p = mv$,the momentum $p_n$ is proportional to $\frac{1}{n}$. Therefore,$\lambda_n = \frac{h}{p_n} \propto n$. When the electron jumps from the third excited state $(n = 4)$ to the ground state $(n = 1)$,the ratio of the wavelengths is $\frac{\lambda_{n=1}}{\lambda_{n=4}} = \frac{1}{4}$.

When an electron in a hydrogen atom jumps from the third excited state to the ground state,the de-Broglie wavelength associated with the electron becomes

Similar Questions

The frequency of the de-Broglie wave of an electron in Bohr's first orbit of a hydrogen atom is . . . . . . . . . . $\times 10^{13} \ Hz$ (nearest integer).
[Given: $R_H$ (Rydberg constant) $= 2.18 \times 10^{-18} \ J$,$h$ (Planck's constant) $= 6.6 \times 10^{-34} \ J \cdot s$]

The wavelengths of electron waves in two orbits are in the ratio $3: 5$. The ratio of the kinetic energy of the electrons will be:

The energy of separation of an electron in a $H$ atom in an excited state is $3.4 \ eV$. The de-Broglie wavelength (in $\mathring{A}$) associated with the above electron is,if the radius of the first orbit of the $H$ atom is $0.53 \ \mathring{A}$.

What is the de Broglie wavelength of a tennis ball weighing $66 \ g$ moving with a velocity of $10 \ m/s$?

$A$ ball weighing $25 \, g$ moves with a velocity of $6.6 \times 10^4 \, cm/sec$. The de Broglie wavelength associated with it is .....

Vedclass Test Series

Exam Paper Generator

Online Exam Module