Question

The energy that should be added to an electron to reduce its Broglie wavelength from one nm to 0.5nm is:

• A. Four times the initial energy
• B. Equal to the initial energy
• C. Twice the initial energy
• D. Thrice the initial energy

Answer 1

Answer: (D)

Thrice the initial energy

Answer 2

: As $\lambda = \frac{h}{\sqrt{2mE}}$

Or $E = \frac{h^{2}}{2m\lambda^{2}}i.e.E \propto \frac{1}{\lambda^{2}}$

Or $\frac{E'}{E} = \frac{\lambda^{2}}{(\lambda')^{2}} = \left( \frac{1}{0.5} \right)^{2} = 4$

Or $E' = 4E$

The energy should be added to decreases the wavelength $= E' - E = 4E - E = 3E$