Question

Calculate the velocity of an electron (mass = 9.11 x 10¯³¹ kg) having a de Broglie wavelength of 269.7 pm
1. 9 x 10⁶ 
2. 6.6 x 10⁶
3. 3.3 x 10⁶ 
4. 2.697 x 10⁶

Answer 1

Correct Answer - Option 4 : 2.697 x 10⁶

Wavelength λ  = 269.7 pm = 269.7 x 10^-12 m = 2.697 x 10^-10 m

\(\lambda \; = \;h/\sqrt {2Em} \)

⇒ 2.697 x 10¯¹⁰ = \(\frac{{6.626 \times {{10}^{ - 34}}}}{{\sqrt {2 \times E \times 9.11 \times {{10}^{ - 31}}} }}\)

E = 3.313 x 10¯¹⁸ J

KE = (1/2) × mv²

3.313 x 10¯¹⁸ = (1/2) × (9.11 x 10¯³¹) v²

v² = 7.2738 x 10¹²

v = 2.697 x 10⁶ m/s