Single Choice

Calculate the de Broglie wavelength for a beam of electron whose energy is 100 eV:

A1:00 AM
B1.23 A
Correct Answer
C2.46 A
DNone of these

Solution

As we know,
E = $$\displaystyle\frac{1}{2}$$mv$$^2$$ = 100 eV = 100 $$\times$$ 1.6 $$\times$$ 10$$^{-19}$$ J

v$$^2$$ = $$\displaystyle\frac{2 E}{m}$$

v = ($$\displaystyle\frac{2 E}{m})^{1/2)}$$

$$\lambda$$ = $$\displaystyle\frac{h}{mv}$$ = $$\displaystyle\frac{h}{\sqrt{2mE}}$$ metre

$$\lambda$$ = $$\displaystyle\frac{6.6 \times 10^{-34}}{(2 \times 9.1 \times 10^{-31} \times 100 \times 1.6 \times 10^{-19}}^{1/2}$$

=1.23 $$\times$$ 10$$^{-10}$$ m =$$ 1.23 A^0$$

SIMILAR QUESTIONS

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