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

6.8 eV

Step-by-step 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 =>
`((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