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Structure Of Atom

Question
CBSEENCH11005253
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The work function for caesium atom is 1.9 eV. Calculate: (a) the threshold wavelength and (b) the threshold frequency of radiation. If the caesium element is irradiated with a wavelength 500 nm, calculate the kinetic energy and velocity of the ejected photoelectron.

Solution

Work function open parentheses straight W subscript 0 close parentheses space equals space hv subscript 0
therefore space space space space space straight v subscript 0 space equals space straight W subscript 0 over straight h                    ...(1)
straight W subscript 0 space space equals space 1.9 space eV space equals space 1.9 space cross times space 1.602 space cross times space 10 to the power of negative 19 end exponent straight J space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space 1 eV space equals 1.602 space cross times space 10 to the power of negative 19 end exponent straight J close square brackets space space space space space space space space straight h space equals space 6.626 space cross times 10 to the power of negative 34 end exponent Js Substituting space the space values space in space eq. space left parenthesis 1 right parenthesis comma space we space have straight v subscript 0 space equals space fraction numerator 1.91 cross times 1.602 space cross times 10 to the power of negative 19 end exponent straight J over denominator 6.626 space cross times 10 to the power of negative 34 end exponent Js end fraction space equals space 4.59 space cross times 10 to the power of 14 straight s to the power of negative 1 end exponent Also comma space straight lambda subscript 0 space equals space straight c over straight v subscript 0 equals space fraction numerator 3.0 cross times 10 to the power of 8 ms to the power of negative 1 end exponent over denominator 4.59 cross times 10 to the power of 14 straight s to the power of negative 1 end exponent end fraction space space space space space space space space space space space equals 6.54 space cross times 10 to the power of negative 7 end exponent straight m space equals 654 cross times 10 to the power of negative 9 end exponent straight m space space space space space space space space space space space equals 654 space nm
We know, 
space KE space equals space straight h left parenthesis straight v minus straight v subscript 0 right parenthesis space equals space hc open parentheses 1 over straight lambda minus 1 over straight lambda subscript 0 close parentheses space space space space space space space... left parenthesis 2 right parenthesis Here space straight lambda space equals space 500 space nm space equals 500 space cross times 10 to the power of negative 9 end exponent straight m space space space space space space space straight lambda subscript 0 space equals space 654 space nm space equals space 654 space cross times 10 to the power of negative 9 end exponent straight m space space space space space space space space straight c space equals space 3 space cross times space 10 to the power of 8 ms to the power of negative 1 end exponent space space space space space space space space straight h space equals space 6.626 space cross times space 10 to the power of negative 34 end exponent Js
Substituting the values in eq. (2), we have
       straight K. straight E. space equals space left parenthesis 6.626 space cross times 10 to the power of negative 34 end exponent Js right parenthesis space left parenthesis 3.0 space cross times 10 to the power of 8 space ms to the power of negative 1 end exponent right parenthesis space space space space space space space space space space space space space space space open square brackets fraction numerator 1 over denominator 500 space cross times 10 to the power of negative 9 end exponent straight m end fraction minus fraction numerator 1 over denominator 654 cross times 10 to the power of negative 9 end exponent straight m end fraction close square brackets space space space space space space space space equals 9.36 space cross times space 10 to the power of negative 20 end exponent straight J
Now space straight K. straight E. space equals space 1 half mv squared space equals space 9.36 space cross times space 10 to the power of negative 20 end exponent kg space straight m squared straight s to the power of negative 2 end exponent
                                                          open square brackets because space space straight J space equals space kgm squared straight s to the power of negative 2 end exponent close square brackets
or space space space 1 half cross times left parenthesis 9.11 space cross times space 10 to the power of negative 31 end exponent space kg right parenthesis straight v squared space space space space space space space space equals 9.36 space cross times space 10 to the power of negative 20 end exponent kg space straight m squared straight s to the power of negative 1 end exponent or space space space space space straight v squared space equals space 2.055 space cross times space 10 to the power of 11 straight m squared straight s to the power of negative 1 end exponent space space space space space space space space space space space space equals space 20.55 space cross times space 10 to the power of 10 straight m squared straight s to the power of negative 2 end exponent or space space space space space space straight v space equals space 4.53 space cross times 10 to the power of 5 ms to the power of negative 1 end exponent

Some More Questions From Structure of Atom Chapter

Who discovered neutron?

What is a neutron?

What is the name of the remaining part of atom except outer orbit?

Name the particles which determine the mass of an element.

What are α-particles?

Why were neutrons discovered very late?

What are the fundamental particles present in a neutral atom having atomic number greater than 1?

Do protons and neutrons have identical mass?

When α-particles are sent through a thin metal foil, most of them go straight through the foil. What inference do you draw from it?

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