CBSE Class 12-science Answered

Bohr's condition, that the angular momentum is an integer multiple of ?.

Electrons can exist only in locations where they interfere constructively.

When an electron is bound to an atom, its wavelength must fit into a small space. Allowed orbits are those in which an electron constructively interferes with itself.

Not all orbits produce constructive interference and thus only certain orbits are allowed (i.e., the orbits are quantized).

By assuming that the electron is described by a wave and a whole number of wavelengths must fit along the circumference of the electron's orbit, we have the equation,

n λ = 2 π r                                 .....................(1)

De Broglie's wavelength is given by,

λ = h/p = h/m_ev                         .....................(2)

Substitute the value of (2) into (1),

nh/m_ev = 2 π r_n                            ...................(3)

L = mvr ( for a circular orbit)         ...................(4)

From (3) and (4) we obtain the quantization of angular momentum as:

L  = m v r_n = n (h/2π) = n ?