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k0ka [10]
3 years ago
15

Red light of wavelength 651 nm produces photoelectrons from a certain photoemissive material. Green light of wavelength 521 nm p

roduces photoelectrons from the same material with 1.50 times the maximum kinetic energy. What is the material's work function?
Physics
2 answers:
damaskus [11]3 years ago
5 0

Given:

wavelength of red light, \lambda _{R} = 651 nm

wavelength of red light, \lambda _{G} = 521 nm

Kinetic energy of green light, K.E _{G} = 1.5K.E_{max}

Solution:

To calculate the work function of the material, \phi

of the material can be calculated by using Einstein's equation for photoelectric effect:

K.E = \frac{hc}{\lambda } - \phi                                    (1)

where,

h = Plank's constant = 6.64\times 10^{-34} J-s

\lambda = wavelength of light

\phi = work function of material

c = speed of light in vacuum =  3\times 10^{8} m/s

Now, for red light:

K.E_{max} = \frac{hc}{\lambda_{R} } - \phi                   (2)

Now, for green light:

1.5K.E_{max} = \frac{hc}{\lambda_{G}} - \phi

K.E_{max} = \frac{2}{3}\frac{hc}{\lambda_{G} } - \phi     (3)

Using eqn (2) and (3):

\frac{1}{3}\phi = hc(\frac{1}{\lambda R} - \frac{2}{3\lambda_{G}})

\phi = 6.64\times 10^{-34}\times 3\times 10^{8}(\frac{1}{651\times 10^{-9}} - \frac{2}{3\times 521^{-9}})

\phi = 1.532\times 10^{-19} J

\phi = \frac{1.532\times 10^{-19}}{1.6\times 10^{-19}}

\phi = 0.958 eV

Answer:

Work function of the material:

\phi = 1.532\times 10^{-19} J  or 0.958 eV  

Mnenie [13.5K]3 years ago
4 0

Answer:

material work function is 0.956 eV

Explanation:

given data

red wavelength 651 nm

green wavelength 521 nm

photo electrons = 1.50 × maximum kinetic energy

to find out

material work function

solution

we know by Einstein photo electric equation  that is

for red light

h ( c / λr ) = Ф +  kinetic energy

for green light

h ( c / λg ) = Ф +  1.50 × kinetic energy

now from both equation put kinetic energy from red to green

h ( c / λg ) = Ф +  1.50 × (h ( c / λr ) - Ф)

Ф =( hc / 0.50) × ( 1.50/ λr  - 1/ λg)

put all value

Ф =( 6.63 ×10^{-34} (3 ×10^{8} )  / 0.50) × ( 1.50/ λr  - 1/ λg)

Ф =( 6.63 ×10^{-34} (3 ×10^{8} ) / 0.50 ) × ( 1.50/ 651×10^{-9}   - 1/ 521 ×10^{-9})

Ф = 1.5305  ×10^{-19} J  × ( 1ev / 1.6 ×10^{-19} J )

Ф = 0.956 eV

material work function is 0.956 eV

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