According to de-Broglie, the de-Broglie wavel | vedclass

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

Question

(C) According to the Bohr quantization condition, the circumference of the orbit is an integral multiple of the de-Broglie wavelength: $2 \pi r_n = n

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) According to the Bohr quantization condition, the circumference of the orbit is an integral multiple of the de-Broglie wavelength: $2 \pi r_n = n \lambda$.Given: $\lambda = 10^{-9} \, m$.The radius of the $n^{th}$ orbit of a hydrogen atom is given by $r_n = n^2 a_0$, where $a_0 \approx 0.529 	imes 10^{-10} \, m$.Substituting $r_n$ into the condition: $2 \pi (n^2 a_0) = n \lambda$.Simplifying for $n$: $n = \frac{\lambda}{2 \pi a_0}$.Substituting the values: $n = \frac{10^{-9}}{2 	imes 3.14159 	imes 0.529 	imes 10^{-10}} \approx \frac{10^{-9}}{3.32 	imes 10^{-10}} \approx 3.01$.Thus, the principal quantum number is $n = 3$.

According to de-Broglie, the de-Broglie wavelength for an electron in an orbit of a hydrogen atom is $10^{-9} \, m$. The principal quantum number for this electron is:

Similar Questions

The number of de-Broglie wavelengths contained in the second Bohr orbit of a hydrogen atom is

In a hydrogen atom,when an electron transitions from the $4^{th}$ orbit to the $2^{nd}$ orbit,the wave number is $20,397 \, cm^{-1}$. What will be the wave number when an electron in a $He^+$ ion transitions from the $4^{th}$ orbit to the $2^{nd}$ orbit?

Imagine that the electron in a hydrogen atom is replaced by a muon $(\mu)$. The mass of the muon particle is $207$ times that of an electron and its charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be ............. $eV$.

In a system, a particle $A$ of mass $m$ and charge $-2q$ is moving in the nearest orbit around a very heavy particle $B$ having charge $+q$. Assuming Bohr's model of the atom to be applicable to this system, the orbital angular velocity of the particle $A$ is

The radius of the first orbit in a hydrogen atom is $5.3 \times 10^{-11} \text{ m}$. The kinetic energy $E_K$, potential energy $E_P$, and total energy $E_T$ of the electron in the first orbit are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module