Question

 

1.1 The work function of sodium is 2.75eV. Calculate the threshold wavelength of light at whigh emission of photoelectrons will first be observed.

1.1 Answer: Threshold wavelength = 451nm

1.2 The threshold wavelength for photoemission of electrons from potassium is 564nm. Calculate the maximum velocity of the photoelectrons that will be emitted when the metal is irradiated by light with a wavelength of 300nm.

1.2 Answer: Maximum velocity = 8.25*10^5 m/s

1.3 The ionization energes of electrons in the three highest occupied molecular orbitals of carbon monoxide are 14.0, 16.8 and 19.7eV. Calculate the kinetric energies in eV of the photoelectrons that will be emitted when CO is irradiated with (a) helium radiation of wavelength 58.4nm and (b) neon radiation of wavelength 74.2nm.

PLEASE explain the answer in detail

1.3 Answer: (a) Kinetic energies of photoelectrons are 7.2, 4.4, and 1.5 eV. (b) Photon energy of neon radiation = 16.7eV. This energy is sufficient to remove electrons only from the highest energy level of CO. These electrons will have a kinetic energy of 2.7eV.

Answer 1

1.1) Work function of sodium ,E= 2.75ev

Work function means minimum energy required to remove an electron from a solid surface

Energy of photon fall on the surface must be equal to this work fuction to remove an electron

This minimum energy of photon is called threshold energy

Energy of a photon given by planck eintein equation

E = h

Where,

h = plank constantant ,4.136×10^-15eV.s

   = frequency of photon

   = c/wavelength

Where, c = speed of light =3.00×10^8m/s

So, planck - Einstein equation can be written as

E = h × c/wavalength

Wavelength = h × c/E

Applying the values

wavelength = 4.136×10^-15 eV.s × 3.00×10^8(m/s)/2.75eV

= 4.512×10^-7m

= 451nm

1.2) First find out the energy of irradiating photon

E = h

    = c/waveength

wavelength = 300nm = 300×10^-9m

c = 3.00×10^8m/s

h = 4.136 × 10^-15eV.s

appying the values

E = 4.136×10^-15eV.s × (3.00×10^8(m/s)/300 ×10^-9m)

= 4.136eV

Now, Calculate the threshold Energy of potassium

threshold wavelength is given as 564nm

Threshold Energy, E = h

E = h × c/wavelength

= 4.136×10^-15eV.s × 3.00×10^8(m/s)/564×10^-9m

   =2.2eV

Kinetic energy of electron = Energy of photon - Threshold Energy

Therefore,

Kinetic energy of electron = 4.136 eV - 2.2eV

= 1.936eV

= 3.101×10^-19J

= 3.101 ×10^-19 kgm^2s^-2

Kinetic energy is given as

K.E = 1/2 m v^2

where,

m = mass of electron , 9.109×10^-31kg

v = velocity of electron

Therefore,

3.101×10^-19kgm^2s^-2 = 1/2(9.109 ×10^-31kg × v^2)

v^2 = 6.80×10^11m2s^-2

v = 8.25×10^5 m/s