Question

Photons of wavelength 115 nm are incident on a metal. The most energetic electrons ejected from the metal are bent into a circular arc of radius 1.04 cm by a magnetic field having a magnitude of 6.50 10-4 T. What is the work function of the metal?

Answer 1

Answer:

6.8 eV

Explanation:

As you know, momentum (P) equals the mass of an object (M) times its velocity (V)

p=mv

Also, the momentum of the particle can be expressed in terms of the radius,

charge and field:

p=mv = qrB

K.Emax = p²/2m= q²r²B²/ 2m

K.Emax= (1.6x$10^{-19}$)² x (0.0104)² x (6.50 x$10^{-4}$)² / (2 x 9.1x$10^{-31}$)

K.E max= 1.16 x $10^{-48}$ / 1.82 x$10^{-30$

K.Emax= 6.37 $10^{-19}$ J

work function 'Ф' = E- K.E max

since E= hc/ λ

Ф= hc/ λ -  K.E max => $\frac{(6.63*10^{-34})(3*10^{8} ) }{115*10^{-9} } - 6.37*10^{-19}$

Ф = 1.09 x $10^{-18}$ J

Ф = 1.09 x $10^{-18}$ / 1.6x$10^{-19}$

Ф =6.8 eV

Therefore, the work function of the metal is 6.8 eV