Question

Energy of electron in orbit of H-atom is -1.51 eV.
Wavelength produced by the electron in same orbit
if 1st orbit of H have radius x
(1) 2pix
(2) 3pix
(3) 6pix
(4) 9pix​

Answer 1

Let energy of an electron in nth orbit of H-atom is -1.51 eV.

energy = -13.6/n² [ from Bohr's theory]

⇒-1.51 = -13.6/n²

⇒n² = 13.6/1.51 ≈ 9

⇒n = 3

now given, radius of 1st orbit of H-atom = x

so, radius of 3rd orbit of H-atom, r = (3)²x = 9x [ as we know, r ∝ n²/Z ]

we know, angular momentum is integral multiple of h/2π

so, mvr = nh/2π

⇒mv9x = 3h/2π

⇒3mvx = h/2π

⇒h/mv = 6πx

from De-broglie's wavelength equation, λ = h/mv

so, λ = 6πx

hence, option (3) is correct choice.

Answer 2

Answer:

Let energy of an electron in nth orbit of H-atom is -1.51 eV.

energy = -13.6/n² [ from Bohr's theory]

⇒-1.51 = -13.6/n²

⇒n² = 13.6/1.51 ≈ 9

⇒n = 3

now given, radius of 1st orbit of H-atom = x

so, radius of 3rd orbit of H-atom, r = (3)²x = 9x [ as we know, r ∝ n²/Z ]

we know, angular momentum is integral multiple of h/2π

so, mvr = nh/2π

⇒mv9x = 3h/2π

⇒3mvx = h/2π

⇒h/mv = 6πx

from De-broglie's wavelength equation, λ = h/mv

so, λ = 6πx

hence, option (3) is correct choice.

Explanation: