AP EAMCET · PHYSICS · Dual Nature of Matter
A photo sensitive metallic surface emits electrons when X-rays of wavelength \(\lambda\) fall on it. The de-Broglie wavelength of the emitted electrons is (Neglect the work function of the surface, \(m\) is mass of the electron, \(h\) is Planck's constant, \(c\) is the velocity of light)
- A \(\sqrt{\frac{2 m c}{h \lambda}}\)
- B \(\sqrt{\frac{h \lambda}{2 m c}}\)
- C \(\sqrt{\frac{ m c}{h \lambda}}\)
- D \(\sqrt{\frac{h \lambda}{ m c}}\)
Answer & Solution
Correct Answer
(B) \(\sqrt{\frac{h \lambda}{2 m c}}\)
Step-by-step Solution
Detailed explanation
de-Broglie wavelength \(\lambda_0=\frac{h}{p}=\frac{h}{\sqrt{2 m E_k}}\) And \(E_K=h v=\frac{h c}{\lambda}\) \(\therefore \quad \lambda_v=\frac{h}{\sqrt{2 m \times \frac{h c}{\lambda}}}=\sqrt{\frac{\lambda h}{2 m c}}\)
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