If the total energy of an electron in a hydro | vedclass

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

Question

(A) The energy of an electron in the $n^{th}$ orbit of a hydrogen atom is given by $E_n = -\frac{13.6}{n^2} 	ext{ eV}$. Given $E_n = -3.4 	ext{ eV}$

Vedclass · Accepted Answer

$6.6 	imes 10^{-10} 	ext{ m}$

Vedclass · Answer

(A) The energy of an electron in the $n^{th}$ orbit of a hydrogen atom is given by $E_n = -\frac{13.6}{n^2} 	ext{ eV}$. Given $E_n = -3.4 	ext{ eV}$,we have $-\frac{13.6}{n^2} = -3.4$,which gives $n^2 = 4$,so $n = 2$. According to Bohr's postulate,$mvr = \frac{nh}{2\pi}$,so the de-Broglie wavelength $\lambda = \frac{h}{mv} = \frac{2\pi r}{n}$. For hydrogen,the radius of the $n^{th}$ orbit is $r_n = 0.529 	imes n^2 	ext{ Å}$. For $n = 2$,$r_2 = 0.529 	imes 2^2 = 2.116 	ext{ Å}$. Substituting these values,$\lambda = \frac{2 	imes \pi 	imes 2.116}{2} = 6.64 	ext{ Å} = 6.64 	imes 10^{-10} 	ext{ m}$.

If the total energy of an electron in a hydrogen atom in an excited state is $-3.4 \text{ eV}$,then the de-Broglie wavelength of the electron is

Similar Questions

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 $0.53 \ \mathring{A}$.

The wavelength of an electron of kinetic energy $4.50 \times 10^{-29} \ J$ is $... \times 10^{-5} \ m$. (Nearest integer) Given: mass of electron is $9 \times 10^{-31} \ kg$,$h = 6.6 \times 10^{-34} \ J \ s$.

What will be the de-Broglie wavelength of an electron moving with a velocity of $1.2 \times 10^5 \ m \ s^{-1}$?

The wavelength associated with a particle of mass $9.109 \times 10^{-31} \ kg$ moving with a velocity of $1.20 \times 10^5 \ m/s$ is ....... meters.

The de Broglie wavelength of a particle $X$ moving with a certain velocity is $1 \ \mathring{A}$. If the mass of $Y$ is $25\%$ of $X$ and its velocity is $75\%$ of $X$,then the de Broglie wavelength of $Y$ will be ........... $\mathring{A}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module