The energy required by electrons, present in the first Bohr orbit of hydrogen atom to be excited to second Bohr orbit is ____

The energy required by electrons present in the first Bohr orbit of hydrogen atom to be excited to second Bohr orbit is

Q. The energy required by electrons, present in the first Bohr orbit of hydrogen atom to be excited to second Bohr orbit is _____ J mol⁻¹.

Given: RH = 2.18 × 10⁻¹¹ ergs.

A. 9.835 × 10¹²

B. 1.635 × 10⁻¹¹

C. 1.635 × 10⁻¹⁸

D. 9.835 × 10⁵

Correct Answer: 9.835 × 10⁵ J mol⁻¹

Explanation

According to Bohr model, energy of electron in nth orbit is:

Energy in first Bohr orbit:
E₁ = −RH

Energy in second Bohr orbit:
E₂ = −RH / 4

Energy required for excitation:
ΔE = E₂ − E₁
ΔE = (−RH / 4) + RH
ΔE = 3RH / 4

Substitute RH = 2.18 × 10⁻¹¹ ergs
ΔE = (3 / 4) × 2.18 × 10⁻¹¹
ΔE = 1.635 × 10⁻¹¹ ergs (per atom)

Convert ergs to joule:
1 erg = 10⁻⁷ J
ΔE = 1.635 × 10⁻¹⁸ J

Energy per mole:
= 1.635 × 10⁻¹⁸ × 6.02 × 10²³
= 9.835 × 10⁵ J mol⁻¹

This question is very important for JEE Main, JEE Advanced and IIT JEE.

Explanation

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