Numericals on Radius, Energy, Frequency, Wavelength and Wave Number

Numericals on Radius, Energy, Frequency, wavelength and wave number from Textbook

Q1.  Find the radius of 4^th orbit of electron in Hydrogen atom (Book question; page # 24, Example # 2.1)

Solution

Z   = 1 (for H atom)

‘n’ = 4 (4^th orbit)

‘a_o’= 0.529 Å

 

Q2. Calculate the energy of an electron in L-shell of hydrogen atom. The value of K 2.18 x 10⁻¹⁸ J/atom 

(Book question; page # 25, Example # 2.2)

Solution

‘n’ = 2 (L-shell corresponds to second energy level)

‘K’= 2.18 x 10⁻¹⁸ J/atom

Q3. Using Bohr model, determine the energy in joule of a photon produced when an electron in hydrogen atom jumps from an orbit n=5 to n=2. 

(Book question; page # 26, Self-Assessment)

Solution

‘n₂’ = 5 

‘n₁’ = 2

Q4. Calculate the wave numbers of photons when electron of a hydrogen atom jumps form 4^th orbit to 2^nd orbit. value of R_H = 1.09678 x 10⁷ m⁻¹.  

(Book question; page # 27, Example 2.3)

Solution

‘n₂’ = 4 

‘n₁’ = 2

Z    = 1

R_H = 1.09678 x 10⁷ m⁻¹

Q5. What is the wave number of a photon produced when an electron falls from n=5 level to n=3 level in hydrogen atom. value of R_H = 1.09678 x 10⁷ m⁻¹.  

(Book question; page # 28, Self-Assessment)

Solution

‘n₂’ = 5 

‘n₁’ = 3

Z     = 1

R_H = 1.09678 x 10⁷ m⁻¹

HOT FAVOURITE QUESTION

*Q6*. A photon of wave number 23 x 10⁵ m⁻¹ is emitted when electron undergoes a transition from a higher orbits to n=2. Determine the orbit form which electron falls and also the spectral line appears in this transition of electron (The value of Rydberg constant is 1.09678 x 10⁷ m⁻¹).

(Book question; page # 49, Assignment)

Solution

R_H = 1.09678 x 10⁷ m⁻¹

Z   = 1

Numericals on Radius, Energy,Frequency, Wavelength and Wave Number from External Source

 

Q1.    If the radius of first Bohr orbit is ‘x’ then calculate the radius of the third orbit of H atom. 

Solution

For given part 

‘n’ = 1 

ao = r1= 0.529 Å= ‘x’ 

r3 = ? 

Radius (r3) = (x) x  32/1 Å      Þ = (x) x  9/1 Å      Þ r3 = 9x Å      

The radius of the third orbit of H atom is 9 times than that of radius of first orbit. 

Q2.  If the radius of first Bohr orbit is ‘x’ Å then calculate the radius of the 2nd orbit of hydrogen. 

Solution

Z = 1 (for H atom)

‘n’ = 2 (2^nd orbit)

‘a_o’= ‘x’ Å

The radius of the second orbit of H atom is 4 times than that of radius of first orbit. 

Q3.Calculate the ratio of radius of second and third orbit of hydrogen atom. (Bohr’s radius =             0.529 Å)

Solution

Z = 1 (for H atom)

‘n’ = 2 (2^nd orbit)

‘n’ = 3 (3^rd orbit)

‘a_o’= 0.529 Å

 

 

Q4. Calculate the ratio of radius of third and fourth orbit of hydrogen atom. (Bohr’s radius = 0.0529 nm)

Solution

Z = 1 (for H atom)

‘n’ = 3 (3^rd orbit)

‘n’ = 4 (4^th orbit)

‘a_o’= 0.0529 nm

 

Q5.Calculate the ratio of the radius of Li²⁺ ion in 3^rd energy level to that of He⁺ ion 2^nd energy level.

Solution 

Q6.What is the wavelength and wave number of radiation that is emitted when a hydrogen atom undergoes a transition from orbit 3 to orbit 1.

Solution

 ‘n₂’ = 3 

‘n₁’ = 1

Z              = 1

R_H  = 1.09678 x 10⁷ m⁻¹

 

Calculation of Wave Number

Calculation of Wave Length 

Q7. Calculate the wave number and wavelength of Balmer series of hydrogen spectrum in which electron jumps from orbit 3 to orbit 2.

 

Solution

Calculation of Wave Number

n₁  = 2

n₂  = 3

R_H = 1.0968553 x 10⁷ m^-1

Z   = 1

Q8.  Calculate the energy of the electron in the ground state and first excited state of the hydrogen atom

Solution

Z for H = 1

n for ground state = 1

n for first excited state = ground state +1 = 1+1=2 (corresponds second energy level)

‘K’= 2.18 x 10⁻¹⁸ J/atom or 13.6 eV

Q9. The energy of electron in the excited state of hydrogen atom is -0.85 eV.  calculate the value of ‘n’ for in the excited state.

Solution 

Assignment

Q1.  Calculate the energy of 1^st, 2^nd and 3^rd orbit of hydrogen atom.

                (Answers; -13.6 eV, -3.41 eV, -1.51 eV)

Q2.  Calculate the radius of 1^st, 2^nd and 3^rd orbit of hydrogen atom.

                (Answers; 0.529°A, 2.226°A, 4.761°A)

Q3. Calculate the angular momentum of 1^st and 2^nd orbit of hydrogen atom.

                (1.054 x 10⁻³⁴ Js, 2.108 x 10⁻³⁴ J.s)

 

Q4. Calculate the wave number of the line in Lyman series when an electron jumps from orbit 3 to orbit 1.

                (Answer; 97613.4 cm⁻¹)

Q5. Calculate the wave number of spectral line of hydrogen gas when an electron jumps from n = 4 to n = 2.

                (Answer; 20654.6 cm⁻¹)