Question 364: Dual Nature of Matter and Radiation

Question

What is the additional energy that should be supplied to a moving electron to reduce its de Broglie wavelength from $$1 \mathrm{~nm}$$ to $$0.5 \mathrm{~nm}$$ ?

Accepted Answer

$$\lambda_1$$ = 1 nm, $$\lambda_2$$ = 0.5 nm
$$	herefore \lambda_2=\frac{\lambda_1}{2}$$
$$\lambda=\frac{h}{p}\quad 	herefore P_2=2P_1$$
Kinetic energy, $$\mathrm{E}=\frac{\mathrm{P}^2}{2 \mathrm{~m}}$$
$$\begin{aligned}
& 	herefore \frac{E_2}{E_1}=\left(\frac{P_2}{P_1}ight)^2=(2)^2=4 \
& 	herefore E_2=4 E_1 \
& 	herefore E_2-E_1=3 E_1
\end{aligned}
$$

Answer

Four times its initial energy.

Answer

Five times its initial energy.

Answer

Two times its initial energy.

Answer

Three times its initial energy.

Dual Nature of Matter and Radiation

What is the additional energy that should be supplied to a moving electron to reduce its de Broglie wavelength from $1 \mathrm{~nm} to 0.5 \mathrm{~nm}$ ?

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