[tex]\bold{\huge{\pink{\underline{ Answer }}}}[/tex]
Concept Used :-
Here, we will use the concept of planks quantum theory .
According to planks quantum theory :-
- The radiant energy is emitted discontinuously in the form of small packets of energy called quanta
- In case of lights, It is called photons
- The amount of energy with each quantum of radiation is directly proportional to the frequency of light
- That is,
- E = hv or E = hc/ λ
- The total amount of energy emitted or a absorbed will be whole number multiple of quantum
- That is,
- E = nhv or nhc/λ
Answer 1 :-
Here,
We have to calculate the energy of an X photon
- The wavelength is 5.00 × 10^-10
- The value of planks constant h is 6.626 × 10^-34 .
According to the planks quantum theory of radiation :-
[tex]\bold{\pink{ E = hv }}[/tex]
[tex]\sf{ E = h}{\sf{\times{\dfrac{c}{λ}}}}[/tex]
- The value of c is 3 × 10^8
Subsitute the required values,
[tex]\sf{ E = 6.626 × 10^{-34} }{\sf{\times{\dfrac{3 × 10^{8}}{5 × 10^{-10}}}}}[/tex]
[tex]\sf{ E = }{\sf{\dfrac{19.87× 10^{-26}}{5 × 10^{-10}}}}[/tex]
[tex]\sf{ E = 3.974 × 10^{-36}}[/tex]
Hence, The energy of an X ray photon is 3.974 × 10^-36
Answer 2 :-
We have ,
- Frequency = 4.57 × 10^14 Hz
- Planks constant = 6.626 × 10^-34
According to the planks quantum theory,
[tex]\bold{\pink{ E = hv }}[/tex]
Subsitute the required values,
[tex]\sf{ E = 6.626 × 10^{-34}× 4.57 × 10^{14}}[/tex]
[tex]\sf{ E = 30.28 × 10^{- 20}}[/tex]
[tex]\sf{ E = 3.028 × 10^{ - 19}}[/tex]
Hence, The energy related to an electron occupying the ground state of hydrogen atoms is 3.028 × 10^-19
Answer 3 :-
We have ,
- Frequency = 4.6 × 10^14 Hz
We know that,
[tex]\bold{\pink{ v = }}{\bold{\pink{\dfrac{ c }{λ}}}}[/tex]
[tex]\sf{ λ = }{\sf{\dfrac{ c }{v}}}[/tex]
Subsitute the required values,
[tex]\sf{ λ = }{\sf{\dfrac{ 3 × 10^{8} }{4.6 × 10^{-14}}}}[/tex]
[tex]\sf{ λ = 0.65 × 10^{22}}[/tex]
Hence, The of this light is 0.65 × 10^22 .
[ Note :- Kindly refer answer in the app]
