For a H atom,the energy transition from n = 1 | vedclass

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

Question

(B) The energy of an electron in a hydrogen-like species is given by $E_n = -13.6 	imes \frac{Z^2}{n^2} \ eV$. For $H$ atom $(Z=1)$,the energy differ

Vedclass · Accepted Answer

$163.2$

Vedclass · Answer

(B) The energy of an electron in a hydrogen-like species is given by $E_n = -13.6 	imes \frac{Z^2}{n^2} \ eV$. For $H$ atom $(Z=1)$,the energy difference $\Delta E = 13.6 	imes Z^2 	imes (\frac{1}{n_1^2} - \frac{1}{n_2^2}) = 13.6 	imes 1^2 	imes (\frac{1}{1^2} - \frac{1}{2^2}) = 13.6 	imes \frac{3}{4} = 10.2 \ eV$. For $Be^{3+}$ ion,the atomic number $Z = 4$. The energy difference for the same transition ($n=1$ to $n=2$) is $\Delta E' = 13.6 	imes Z^2 	imes (\frac{1}{n_1^2} - \frac{1}{n_2^2})$. $\Delta E' = 13.6 	imes 4^2 	imes (\frac{1}{1^2} - \frac{1}{2^2}) = 13.6 	imes 16 	imes \frac{3}{4} = 13.6 	imes 4 	imes 3 = 163.2 \ eV$.

For a $H$ atom,the energy transition from $n = 1$ to $n = 2$ is $10.2 \ eV$. What will be the energy for the same transition in $Be^{3+}$ ion?

Similar Questions

Calculate the ratio of the radius of the $2^{nd}$ and $3^{rd}$ orbit of a hydrogen atom. (Note: $r_n \propto n^2$)

Neon gas is generally used in sign boards. If it emits strongly at $616 \, nm$,calculate $(a)$ the frequency of emission,$(b)$ distance traveled by this radiation in $30 \, s$,$(c)$ energy of a quantum,and $(d)$ number of quanta present if it produces $2 \, J$ of energy.

The ionization energy of a hydrogen atom is $13.6 \ eV$. The energy required to excite the electron in a hydrogen atom from the ground state $(n=1)$ to the first excited state $(n=2)$ is (Note: The question asks for energy per atom in Joules. Given $1 \ eV = 1.602 \times 10^{-19} \ J$)

Find the radius of the first,second,and third orbits of the hydrogen atom.

The energy of the third orbit of $Li^{2+}$ ion (in $J$) is

Vedclass Test Series

Exam Paper Generator

Online Exam Module