Related Formula
K = (hc)/(λ) - φ$$K_{\max} = \frac{hc}{\lambda} - \phi$$
p = 2m K$$p = \sqrt{2m K_{\max}}$$
R = (p)/(eB)$$R = \frac{p}{eB}$$
d = 2R$d = 2R$
Core Logic
According to Einstein's photoelectric equation, the maximum kinetic energy of the emitted photoelectron is:
K = (hc)/(λ) - φ$$K_{\max} = \frac{hc}{\lambda} - \phi$$
The momentum p$p$ corresponding to this kinetic energy is:
p = 2m K = √(2m ((hc)/(λ) - φ))$$p = \sqrt{2m K_{\max}} = \sqrt{2m \left(\frac{hc}{\lambda} - \phi\right)}$$
The electron is emitted normally to the plate and enters a perpendicular constant magnetic field B$B$. It describes a circular arc (semicircle) and hits back the plate at point B. The distance between A and B is the diameter of this circular trajectory:
dAB = 2R = 2 ( (p)/(eB) ) = 2√(2m((hc)/(λ) - φ))eB$$d_{AB} = 2R = 2 \left( \frac{p}{eB} \right) = \frac{2\sqrt{2m\left(\frac{hc}{\lambda} - \phi\right)}}{eB}$$
To align this with the options, move the factor of 2 inside the square root (2 = √(4)$2 = \sqrt{4}$):
dAB = √(4 × 2m((hc)/(λ) - φ))eB = √(8m((hc)/(λ) - φ))eB$$d_{AB} = \frac{\sqrt{4 \times 2m\left(\frac{hc}{\lambda} - \phi\right)}}{eB} = \frac{\sqrt{8m\left(\frac{hc}{\lambda} - \phi\right)}}{eB}$$Step 1: Final Conclusion
The distance between points A and B is
$
Step 1: Final Conclusion
The distance between points A and B is $
\sqrt{8m\left(\frac{hc}{\lambda} - \phi\right)} / eB
. Pattern Recognition
When a particle is launched perpendicularly from a flat boundary into a perpendicular magnetic field, it describes a semicircle and exits/re-hits the boundary at a distance equal to the diameter
$.
Pattern Recognition
When a particle is launched perpendicularly from a flat boundary into a perpendicular magnetic field, it describes a semicircle and exits/re-hits the boundary at a distance equal to the diameter $
2R = 2\frac{p}{qB}
. Taking coefficients inside square roots converts$. Taking coefficients inside square roots converts $2 \sqrt{2x}
to$ to $\sqrt{8x}$.
Chapter Mix
Class 12 Physics: Dual Nature of Matter and Radiation
Class 12 Physics: Moving Charges and Magnetism
