Question

The circumference of the second orbit of an atom or ion having a single electron is $4\times {10}^{-9}\mathrm{m}$ The de-Broglie wavelength of electrons revolving in this orbit should be

• A. $1\times {10}^{-9}\mathrm{m}$
• B. $2\times {10}^{-9}\mathrm{m}$
• C. $4\times {10}^{-9}\mathrm{m}$
• D. $8\times {10}^{-9}\mathrm{m}$

Answer 1

The correct option is B

$2\times {10}^{-9}\mathrm{m}$

The explanation for the correct option:

Option (B): $2\times {10}^{-9}\mathrm{m}$

Step 1: Analyzing Given data

1. Circumference of the orbit= $4\times {10}^{-9}\mathrm{m}$
2. The shell number= 2

Step 2: Calculation of circumference of the orbit

1. As from de-Broglie the circumference of the orbit is equal to $\mathrm{n\lambda }$.
2. So $2\mathrm{\pi r}=\mathrm{n\lambda }$ putting the values in the given formula, we calculate the wavelength of electron.
3. So, $\mathrm{\lambda }=\frac{4\times {10}^{-9}}{2}\mathrm{m}=2\times {10}^{-9}\mathrm{m}$

Therefore, The wavelength is$2\times {10}^{-9}\mathrm{m}$.

Hence, option (B) is correct.