In a hydrogen atom, the minimum energy requir | vedclass

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

Question

(C) According to Bohr's theory, the energy of an electron in the $n^{th}$ orbit of a hydrogen-like atom is given by $E_n = -13.6 \frac{Z^2}{n^2} \ eV$

Vedclass · Accepted Answer

$1.9$

Vedclass · Answer

(C) According to Bohr's theory, the energy of an electron in the $n^{th}$ orbit of a hydrogen-like atom is given by $E_n = -13.6 \frac{Z^2}{n^2} \ eV$. The energy required to excite an electron from orbit $n_1$ to $n_2$ is $\Delta E = E_{n_2} - E_{n_1} = 13.6 \ Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight) \ eV$. For a hydrogen atom, $Z = 1$, $n_1 = 2$, and $n_2 = 3$. Substituting these values: $\Delta E = 13.6 	imes 1^2 \left( \frac{1}{2^2} - \frac{1}{3^2} ight) \ eV$ $\Delta E = 13.6 \left( \frac{1}{4} - \frac{1}{9} ight) \ eV$ $\Delta E = 13.6 \left( \frac{9 - 4}{36} ight) \ eV$ $\Delta E = 13.6 	imes \frac{5}{36} \ eV \approx 1.888 \ eV \approx 1.9 \ eV$.

In a hydrogen atom, the minimum energy required to excite an electron from the $2^{nd}$ orbit to the $3^{rd}$ orbit is: (in $eV$)

Similar Questions

Which of the following statements regarding the energy of the stationary state is true in the following one-electron system?

The wave number of the spectral line in the emission spectrum of hydrogen will be equal to $\frac{8}{9}$ times the Rydberg's constant if the electron jumps from

In the Bohr series of lines of the hydrogen spectrum,the third line from the red end corresponds to which one of the following inter-orbit jumps of the electron for Bohr orbits in an atom of hydrogen?

Which transition in a $H$ atom emits the maximum energy?

The watermelon model of the atom was proposed by:

Vedclass Test Series

Exam Paper Generator

Online Exam Module