Show that the circumference of the Bohr orbit for the hydrogen atom is

1.	Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de-Broglie wave length associated with the electron revolving around the orbit.
Answer» According to the Bohr's principle of quantization of angular momentum (mvr) of a moving electron, we can write mvr = n h/2π Where m is the mass of the electron v is the velocity of the electron r is radius of the orbit h is the Planck's constant n is an integral number (n = 1, 2, 3,....) The de Broglie wave length associated with the electron is given by λ = h/mv From the two equations, we can write mvr/mv = {nh/2π}/{h/λ} or, 2πr = nλ Hence, circumference of the orbit = Integral multiple of the de Broglie wavelength.

Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de-Broglie wave length associated with the electron revolving around the orbit.

Answer»

According to the Bohr's principle of quantization of angular momentum (mvr) of a moving electron, we can write

mvr = n h/2π

Where m is the mass of the electron

v is the velocity of the electron

r is radius of the orbit

h is the Planck's constant

n is an integral number (n = 1, 2, 3,....)

The de Broglie wave length associated with the electron is given by

λ = h/mv

From the two equations, we can write

mvr/mv = {nh/2π}/{h/λ}

or, 2πr = nλ

Hence, circumference of the orbit = Integral multiple of the de Broglie wavelength.