The energy of an electron in the first Bohr orbit of hydrogen atom is - 2 . 18 × 10 ^ - 18 J Its energy in the third Bohr orbit is _______ .

Correct answer: C. Three times of this value The energy of an electron in the n ^ th Bohr orbit of a hydrogen atom can be calculated using the formula: E _ n = - 2 . 18 × 10 ^ - 18 Z ^ 2 n ^ 2 WherenistheprincipalquantumnumberoftheBohrorbit . E _ n α 1 n ^ 2 E _ n α(1)/(9) Therefore, the energy of the electron in the third Bohr orbit of a hydrogen atom is Three times of this value.

JEE Main 202313 AprilMorning Shift

Exam: JEE Main
Year: 2023
Date: 13 April
Shift: Morning Shift
Subject: Chemistry
Chapter: Structure of Atom

JEE Main 2023 · 13 April · Morning Shift · Chemistry · Structure of Atom

The energy of an electron in the first Bohr orbit of hydrogen atom...

The energy of an electron in the first Bohr orbit of hydrogen atom is $- 2 . 18 \times {10}^{- 18}J$ Its energy in the third Bohr orbit is $_______ .$

Options

A $\dfrac{1}{9}th$ of the value
B $\dfrac{1}{27}$ of this value
C
Three times of this value
D
One third of this value

Correct answer

Three times of this value

Step-by-step solution

The energy of an electron in the ${n}^{th}$ Bohr orbit of a hydrogen atom can be calculated using the formula:

${E}_{n} = \dfrac{- 2 . 18 \times {10}^{- 18}{Z}^{2}}{{n}^{2}}WherenistheprincipalquantumnumberoftheBohrorbit . {E}_{n}\alpha\dfrac{1}{{n}^{2}}{E}_{n}\alpha\dfrac{1}{9}$

Therefore, the energy of the electron in the third Bohr orbit of a hydrogen atom is Three times of this value.

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