Titanium metal requires a photon with a minimum energy of 6 .9 4 * 1 0 - 1 9 J t

Question

Titanium metal requires a photon with a minimum energy of 6 .9 4 * 1 0 - 1 9 J to emit electrons. ( a ) What is the minimum frequency of light necessary to emit electrons from titanium via the photoelectric effect? ( b ) What is the wavelength of this light? ( c ) Is it possible to eject electrons from titanium metal using visible light? ( d ) If titanium is irradiated with light of wavelength 233 nm, what is the maximum possible kinetic energy of the emitted electrons? ( d ) What is the maxi - mum number of electrons that can be freed by a burst of light whose total energy is 2 . 0 0 m J ?

Explanation / Answer

Titanium metal requires a photon with a minimum energy of 6 .9 4 * 1 0 - 1 9 J to emit electrons.

( a ) What is the minimum frequency of light necessary to emit electrons from titanium via the photoelectric effect?

Solution :- formula to calculate the frequency is

E=h*v

V=E/h

V= 6.94*10^-19 J / 6.626*10^-34 J .s

V= 1.05*10^15 s-1

So the frequency of the light is 1.05*10^15 s-1

( b ) What is the wavelength of this light?

Solution :- wavelength l = c/v

                                            = 3*10^8 m per s / 1.05*10^15 s-1

                                          = 2.86*10^-7 m

Lets convert m to nm

2.86*10^-7 m * 1*10^9 m / 1 m = 286 nm

( c ) Is it possible to eject electrons from titanium metal using visible light?

Solution :-

Since the wavelength of the radiation is not fall under the visible light wavelength therefore it is not possible to eject the electron using the visible light.

( d ) If titanium is irradiated with light of wavelength 233 nm, what is the maximum possible kinetic energy of the emitted electrons?

Solution :- using the 233 nm wavelength lets calculate the energy

E= hc/l

= 3*10^8 m per s * 6.626*10^-34 J .s / 2.33*10^-7 m

= 8.53*10^-19 J

Since the energy is high therefore 233 nm light can eject the electron

( e ) What is the maxi - mum number of electrons that can be freed by a burst of light whose total energy is 2 . 0 0 m J ?

Solution :-

2 mJ * 0.001 J / 1 mJ = 0.002 J

1 electron = 6.94*10^-19 J

Therefore

0.002 J * 1 e- / 6.94*10^-19 J = 2.88*10615 electrons

So it can eject 2.88*10^15 electrons

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