The De Broglie wavelength lambda of an electr | vedclass

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

Question

(A) According to Bohr's postulate,the angular momentum of an electron in an orbit is given by $mvr = \frac{nh}{2\pi}$.Rearranging this,we get $2\pi r

Vedclass · Accepted Answer

$4\pi r_1$

Vedclass · Answer

(A) According to Bohr's postulate,the angular momentum of an electron in an orbit is given by $mvr = \frac{nh}{2\pi}$.Rearranging this,we get $2\pi r = \frac{nh}{mv}$.Since the De Broglie wavelength is $\lambda = \frac{h}{mv}$,we can substitute this into the equation to get $2\pi r = n\lambda$,or $\lambda = \frac{2\pi r}{n}$.For the $2^{nd}$ Bohr orbit,$n = 2$.The radius of the $n^{th}$ orbit is given by $r_n = n^2 r_1$,where $r_1$ is the radius of the first Bohr orbit.For $n = 2$,$r_2 = 2^2 r_1 = 4r_1$.Substituting these values into the wavelength formula: $\lambda = \frac{2\pi (4r_1)}{2} = 4\pi r_1$.

The De Broglie wavelength $\lambda$ of an electron in the $2^{nd}$ Bohr orbit is:

Similar Questions

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

The de Broglie wavelength associated with a ball of mass $1 \, kg$ having kinetic energy $0.5 \, J$ is

The wavelength of an electron and a neutron will become equal when the velocity of the electron is $x$ times the velocity of the neutron. The value of $x$ is (Nearest Integer). (Mass of electron is $9.1 \times 10^{-31} \ kg$ and mass of neutron is $1.6 \times 10^{-27} \ kg$)

What is the de Broglie wavelength of an electron in the $n^{th}$ Bohr orbit?

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) $= 6.6 \times 10^{-34} \ J \cdot s$]

Vedclass Test Series

Exam Paper Generator

Online Exam Module