Question

An electron of He⁺ is present in 3^rd excited state. Find its de-Broglie wavelength. 

(1) 6.64 Å 

(2) 1.66 Å 

(3) 3.32 Å 

(4) 13.28 Å

Answer 1

Correct option is: (1) 6.64 Å 

\(n\lambda = 2\pi r\)

For 3^rd excited state, n = 4

\(4 \lambda = 2 \times \pi \times a \frac{n^2}{z}\)

\(4 \lambda = 2 \times \pi \times 0.529 \frac{16}{2}\mathring{A}\)

\(\lambda = 2 \times 3.14 \times 0.529 \times 2 \ \mathring{A} = 6.64 \mathring{A}\)