The wavelength of electrons accelerated from rest through a potential difference of 40 kV is x $\times$ 10$-$12 m. The value of x is ___________. (Nearest integer)
Give : Mass of electron = 9.1 $\times$ 10$-$31 kg
Charge on an electron = 1.6 $\times$ 10$-$19 C
Planck's constant = 6.63 $\times$ 10$-$34 Js
Answer (integer)
6
Solution
Wavelength of electron is given by<br><br>$\lambda = {h \over {\sqrt {2mqV} }}$<br><br>Here q = charge on electron, V = potential difference<br><br>$$\lambda = {{6.63 \times {{10}^{ - 34}}} \over {\sqrt {2 \times 9.1 \times {{10}^{ - 31}} \times 1.6 \times {{10}^{ - 19}} \times 40 \times {{10}^3}} }}$$<br><br>$$ = {{6.63 \times {{10}^{ - 34}}} \over {\sqrt {1164.8 \times {{10}^{ - 47}}} }} = 6.144 \times {10^{ - 12}} \approx 6 \times {10^{ - 12}}$$<br><br>x = 6<br><br>OR<br><br>$\lambda = {{12.3} \over {\sqrt V }}\mathop A\limits^o$<br><br>$= {{12.3} \over {200}} = 6.15 \times {10^{ - 12}}$ m<br><br>$\therefore$ Ans. is 6
About this question
Subject: Chemistry · Chapter: Atomic Structure · Topic: Bohr's Model
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