Chemistry Class 11 NCERT Solutions: Chapter 2 Structure of Atom Part 6

Q: 16. (i) The energy associated with the first orbit in the hydrogen atom is Equation What is the energy associated with the fifth orbit?

(ii) Calculate the radius of Bohr’s fifth orbit for hydrogen atom.

Answer:

(i) Energy associated with the first orbit in the hydrogen atom is calculated as:

Equation

Equation

(ii) Radius of Bohr’s Equation orbit for hydrogen atom is given by,

Equation

For,

Equation

Equation

Equation

Q: 17. Calculate the wave number for the longest wavelength transition in the Balmer series of atomic hydrogen.

Answer:

For the Balmer series, Equation thus, the expression of wavenumber Equation is given by,

Equation

Wave number Equation is inversely proportional to wavelength of transition. Hence, for the longest wavelength transition, Equation has to be the smallest.

For Equation to be minimum, Equation should be minimum. For the balmer series, a transition from Equation is allowed. Hence, taking Equation

Equation

Equation

Equation

Equation

Equation

Q: 18. What is the energy in joules, required to shift the electron of the hydrogen from the first Bohr orbit to the fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is Equation

Answer:

Energy (E) of the Equation Bohr orbit of an atom is given by,

Equation

Where,

Z=atomic number of the atom

Ground state energy Equation

Equation

Equation

Equation

Energy required to shift the electron from Equation is given as:

Equation

Equation

Equation

Equation

Wavelength of emitted light Equation

Equation

Equation

Q: 19. The electron energy in hydrogen atom is given by Equation Calculate the energy required to remove an electron completely from the Equation orbit. What is the longest wavelength of light in cm that can be used to cause this transition?

Answer:

Given,

Equation

Energy required for ionization from Equation is given by,

Equation

Equation

Equation

Equation

Equation

Equation

Here, Equation is the longest wavelength causing the transition.

Equation

Equation

Equation

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