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H,He^(+), Li^(2+) are examples of atoms ...

H,`He^(+), Li^(2+)` are examples of atoms or ions with one electron each . The energy of such atoms when in the n-th energy state (according to Bohr,s theory , n=1,2,3…. =principal quantum number ) is `E_n =(-13.6 Z^2)/(n^2) eV (1 eV =1.6xx10^(-19)J)`.
For the ground state ,n=1 . in order to raise the atom from the ground state to n=f , the suitable incident light should have a wavelength given by `lambda=(hc)/(E_f-E_1)`. But the atom cannot stay permanently in the f-energy state, ultimately , it comes to the ground state by radiating the extra energy ,`E_f-E_1` as electromagnetic radiation .
The electron of the atom comes from n=f to n=1 in one or more steps using the permitted energy levels .
As a result there is a possibility of emission of radiation with more than one wavelength from the atom.
Planck's constant `=6.63 xx10^(-34)J*s` and velocity of light `c=3xx10^(8)m*s^(-1)`.
(i)What is the wavelength of the light incident on the atom to raise it to the fourth quantum level from ground state ?

A

952 Å

B

975 Å

C

1027 Å

D

1219 Å

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • H, He^(+), Li^(2+) are examples of atoms or ions with one electron each . The energy of such atoms when in the n-th energy state (according to Bohr,s theory , n=1,2,3…. =principal quantum number ) is E_n =(13.6 Z^2)/(n^2) eV (1 eV =1.6xx10^(-19)J) . For the ground state ,n=1 . in order to raise the atom from the ground state to n=f , the suitable incident light should have a wavelength given by lambda=(hc)/(E_f-E_1) . But the atom cannot stay permanently in the f-energy state, ultimately , it comes to the ground state by radiating the extra energy , E_f-E_1 as electromagnetic radiation . The electron of the atom comes from n=f to n=1 in one or more steps using the permitted energy levels . As a result there is a possibility of emission of radiation with more than one wavelength from the atom. Planck's constant =6.63 xx10^(-34)J*s and velocity of light c=3xx10^(8)m*s^(-1) . (iii) What is the value of the maximum wavelength in example (ii) ?

    A
    952 Å
    B
    975 Å
    C
    6577 Å
    D
    18830 Å

  • H, He^(+), Li^(2+) are examples of atoms or ions with one electron each . The energy of such atoms when in the n-th energy state (according to Bohr,s theory , n=1,2,3…. =principal quantum number ) is E_n =(13.6 Z^2)/(n^2) eV (1 eV =1.6xx10^(-19)J) . For the ground state ,n=1 . in order to raise the atom from the ground state to n=f , the suitable incident light should have a wavelength given by lambda=(hc)/(E_f-E_1) . But the atom cannot stay permanently in the f-energy state, ultimately , it comes to the ground state by radiating the extra energy , E_f-E_1 as electromagnetic radiation . The electron of the atom comes from n=f to n=1 in one or more steps using the permitted energy levels . As a result there is a possibility of emission of radiation with more than one wavelength from the atom. Planck's constant =6.63 xx10^(-34)J*s and velocity of light c=3xx10^(8)m*s^(-1) . (iv) What is the value of the minimum wavelength in example (ii) ?

    A
    952 Å
    B
    975 Å
    C
    6577 Å
    D
    18830 Å

  • H, He^(+), Li^(2+) are examples of atoms or ions with one electron each . The energy of such atoms when in the n-th energy state (according to Bohr,s theory , n=1,2,3…. =principal quantum number ) is E_n =(13.6 Z^2)/(n^2) eV (1 eV =1.6xx10^(-19)J) . For the ground state ,n=1 . in order to raise the atom from the ground state to n=f , the suitable incident light should have a wavelength given by lambda=(hc)/(E_f-E_1) . But the atom cannot stay permanently in the f-energy state, ultimately , it comes to the ground state by radiating the extra energy , E_f-E_1 as electromagnetic radiation . The electron of the atom comes from n=f to n=1 in one or more steps using the permitted energy levels . As a result there is a possibility of emission of radiation with more than one wavelength from the atom. Planck's constant =6.63 xx10^(-34)J*s and velocity of light c=3xx10^(8)m*s^(-1) . For what wavelength of incident radiation He^+ ion will be raised to fourth quantum state from ground state?

    A
    243.7 Å
    B
    487.5 Å
    C
    731.2 Å
    D
    975 Å

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