Question

De Broglie wavelength of an electron orbiting in the n = 2 state of hydrogen atom is close to ______. (given Bohr radius = 0.052 nm)

विकल्प

• 0.067 nm

• 0.67 nm

• 1.67 nm

• 2.67 nm

Answer 1

De Broglie wavelength of an electron orbiting in the n = 2 state of hydrogen atom is close to 0.67 nm.

Explanation:

Given: Z = 1

n = 2

v = `2.18 xx 10^6 Z/n`     ...(From Bohr’s theory)

= `2.18 xx 10^6 xx 1/2`

= 1.09 × 10⁶ m/s

De Broglie wavelength, λ = `h/(mv)`

= `(6.625 xx 10^-34)/(9.1 xx 10^-31 xx 1.06 xx 10^6)`

= `(6.625 xx 10^-34)/(9.919 xx 10^-25)`

= 0.667 × 10⁻⁹ m   ...(∵ 1 nm = 10⁻⁹ m)

= 0.67 nm