Question

. If the velocity of hydrogen molecule is 5 x 104 cm sec ), then its de Broglie wavelength is (1) 2 A (2) 4 A (3) 8 A (4) 100 A ​

Answer 1

Answer :-

It's De-brogile wavelength is 4 Å [Option.2]

Explanation :-

We have :-

→ Velocity of hydrogen molecule

= 5 × 10⁴ cm/s = 5 × 10² m/s

→ Molar mass of Hydrogen = 2 g/mol

→ Planck's contant = 6.62 × 10⁻³⁴ Js

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Firstly, let's calculate the mass of 1 molecule of hydrogen .

= Molar mass/Avogadro Number

= 2/(6.022 × 10²³)

= 2/6.022 × 10⁻²³

= 0.33 × 10⁻²³ g

= 0.33 × 10⁻²⁶ kg

= 3.33 × 10⁻²⁷ kg

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Now, according to De-Brogile equation :-

λ = h/mv

⇒ λ = (6.62 × 10⁻³⁴)/(3.33 × 10⁻²⁷ × 5 × 10²)

⇒ λ = 6.626/16.65 × 10⁻³⁴⁺²⁷⁻²

⇒ λ = 0.4 × 10⁻⁹ m

⇒ λ = 4 × 10⁻¹⁰ m

On, converting the unit of wavelength from metre to Angstrom .

⇒ 10⁻¹⁰ m = 1 Å

⇒ 4 × 10⁻¹⁰ m = 4(1)

⇒ 4 Å