The figure shows standing de-Broglie waves due to the revolution of electron in a certain orbit of hydrogen atom. Then, the expression for the orbit radius is (All notations have their usual meanings )

Step-by-step solution

According to de-Broglie, the circumference of a stationary orbit must be an integral number of wavelengths. aligned & n =2 r_ n & Also, angular momentum, m v_ n r_ n = n h 2 & m e² 2 n h ₀ r_ n = n h 2 [ v_ n = e² 2 n h ₀ ] & r_ n = n² h² ₀ m e² = n² h² ₀ m e² aligned Here, number of standing waves, n=6 _ n = (6)² h² ₀ m e² = 36 h² ₀ m e²