Numerical on Energy calculkation and de broglie equation and Heisenberg equation
NUMERICALS ON ENERGY:
1. What are the frequency and wavelength of a photon emitted during a transition from n=5 to
n=2 state in the H-atom. (4.578X10-19 J/atom, 434 nm)
2. Calculate the longest wavelength of light that will be needed to remove an e- from third orbit
0f He+ ion. (205.5 nm)
HINT : longest wavelength is from infinity to that shell)
3. 1) The energy associated with the first orbit in the H-atom is -2.17X10 -18 J/atom. What is the
energy associated with the fifth orbit? (Ans: 1) – 8.68X10-20 J)
2) Calculate the radius of Bohr’s fifth orbit of H-atom? ( 1.3225nm)
4. Calculate the energy associated with the first orbit of He+. What is the radius of this orbit?
E1 = - 8.72 X 10-18 J/atom, r1 = 0.02645 nm
5 What is the max number of emission lines when the excited e- of H-atom in n=6 drops to the
ground state?
Ans: Use the equation n(n-1)/2 = 15 0r (n2-n1)(n2-n1+1)/2
6. The radius of an orbital hydrogen atom is 0.85nm calculate velocity of electron in this orbital .
(5.5X105 m/s)
7. Using the Bohr model, determine the energy in joules of the photon produced when an electron in
a He+ moves from the orbit with n = 5 to n = 2. (-1.83 × 10-18 J)
8. The electron volt (eV) is a convenient unit of energy for expressing atomic-scale energies. It is the
amount of energy that an electron gains when subjected to a potential of 1
volt; 1eV=1.602×10−19J1eV=1.602×10−19J. Using the Bohr model, determine the energy, in electron
volts, of the photon produced when an electron in a hydrogen atom moves from the orbit
with n=5 to n=2. (2.856 eV)
9. Which of the electron transitions below will result in the emission of light with the longest
wavelength?
a. n = 1 to n = 3 b. n = 4 to n = 3 c. n = 3 to n = 2
d. n = 3 to n = 1 e. n = 2 to n = 3
10. 10 The He+ ion is a one-electron system similar to hydrogen, except that it has 2 protons.
Calculate the wavelength of the longest wavelength line in each of the first three spectroscopic
series (n=1,2,3)
Longest wavelength line occurs when the energy difference between two states is least. Hence, the
longest 'n' from higher states is line reaching from 'n+1' as the energy difference is least. ... Case-
c: n=3 ... The wavelength of the longest wavelength line in each of the first three
spectroscopic series is ...
11. RYDBERG EQUATION :
What is the wavelength of light emitted when the e- in the H-atom undergoes transitions from an
energy level n=4 to n=2? What is the colour of the radiation? (4.86X10-5cm)
11. In the Rydberg’s equation a spectral lines corresponds to n1=3 and n2=5 . 1) Calculate the
wavelength and frequency of this spectral line.
2) To which spectral series does this line belongs?
3) In which region of the EM spectrum will this line fall?
ANS: 1) λ = 1282nm and ν = 2.34X1014 hertz 2) Paschen series 3) IR region.
DE-Broglie’s Equation :
Q1. A beam of helium atoms moves with a velocity of 2X 103 m/s . find the wavelength of the particle
constituting the beam.
Q2. If the velocity of electron in Bohr's first orbit is 2.19X106 m/s, calculate the de broglie wavelength
associated with it.
Q3. Calculate the kinetic energy of the moving electron which was the wavelength of 4.8 pm.
Q4. Calculate the wavelength of an electron that has been accelerated in a particle accelerator
through a potential difference of hundred million volts(1eV = 1.6X10-19 C).
Q5. What will be the wavelength of a ball of mass 0.1 kg moving with a velocity of 10 m/ s.
Q6. Calculate the kinetic energy of an Alpha particle which has a wavelength of 12 pm.
Q7. A tennis ball of mass 6X10-2Kg is moving with a speed of 62m/s. Calculate the wavelength
associated with this tennis ball .Will it exhibit wave nature? (1.8X10-34 m, No)
Q8. Calculate the de-broglie wavelength of an electron moving at 1% speed of light. (2.43X10 -10 m)
Q9. Calculate the wavelength of an electron moving with a velocity of 2.05X107 m/s
Ans: 3.55X10-11 m
Q10. Calculate the mass of a photon of sodium light having wavelength of 5894Amstrong and velocity
3X108 m/s. 3.74X10-36 Kg
Q11. Two particles A and B are in motion . If the wavelength associated with particle A is 5X10 -8m,
calculate the wavelength of particle B if its momentum is half of A.
Q12. An electron is moving with a K.E of 2.275X10-25J . Calculate its de-broglie’s wavelength.
1.026X10-6 m
Q13. Calculate the wavelengty of an e- which has been accelerated to a potential difference of 100
million volts( 1eV = 1.6X10-19C). 1.234X10-13 m
HEISENBERG UNCERTAINITY PRINCIPLE
Q1. Calculate the uncertainty in the position of an electron if uncertainty in its velocity is 1) 0.001%)
ii) zero (Given velocity of electron = 300m/s.
Q2. An electron has a speed of 500 metre per second with uncertainty of 0.02% what is the
uncertainty in locating its position.
Q3. A golf ball has a mass of 40 grams and speed of 45 metre per second . If the speed can be
measured with accuracy of 2% calculate the uncertainty its position.
Q4. A microscope using suitable photons is employed to locate an electron in an atom within distance
of 0.1 amstrong. What is the uncertainty involved in the measurement at the velocity?
Q5. Calculate the uncertainity in the position of an e- , if the uncertainity in its velocity is 5.7X10 5
m/s. 1.012X10-10m
Q6. Calculate the uncertainity in the velocity of a wagon of mass 2000 Kg whose position is known to
an accuracy of +- 10m. Ans: 2.636X10-39 m/s.
Q7. On the basis of Heisenberg uncertainity principle prove that an electron cannot exist within the
atomic nucleus. 5.77X1010 m/s
