Question

The number of waves in the third orbit of H atom is 1) 1 2)2 3)4 4)3

Answer 1

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Answer 2

Answer: The correct option is 4.

Explanation: Number of waves in an orbit is written as:

$\text{Number of waves}=\frac{\text{Circumference of the orbit}}{Wavelength}}$

$\text{Number of waves}=\frac{2\pi r}{\lambda }$

Using de - Broglie equation:

$\lambda =\frac{h}{mv}$

Putting the value of wavelength in above equation we get,

$\text{Number of waves}=\frac{2\pi (mvr)}{h}$      ....(1)

Now, angular momentum of the third shell is written as:

$\text{Angular Momentum}=\frac{nh}{2\pi }$

Putting n = 3 in above equation we get,

$mvr=\frac{3h}{2\pi }$

Putting the value of (mvr) in equation 1, we get

$\text{Number of waves}=\frac{2\pi \times (3h)}{h\times 2\pi }$

Number of waves = 3