Dual Nature Of Matter Question 9

Question 9 - 30 January - Shift 2

An electron accelerated through a potential difference $V_1$ has a de-Broglie wavelength of $\lambda$. When the potential is changed to $V_2$, its de-Broglie wavelength increases by $50 %$. The value of $(\frac{V_1}{V_2})$ is equal to :

(1) 3

(2) $\frac{9}{4}$

(3) $\frac{3}{2}$

(4) 4

Show Answer

Answer: (2)

Solution:

Formula: De Broglie wavelength

$KE=\frac{P^{2}}{2 m}, P=\frac{h}{\lambda}$

$eV_1=\frac{(\frac{h}{\lambda})^{2}}{2 m}$

$eV_2=\frac{(\frac{h}{1.5 \lambda})^{2}}{2 m}$

$\frac{V_1}{V_2}=(1.5)^{2}=\frac{9}{4}$