Advertisements
Advertisements
Question
Assume that there is no repulsive force between the electrons in an atom but the force between positive and negative charges is given by Coulomb’s law as usual. Under such circumstances, calculate the ground state energy of a He-atom.
Advertisements
Solution
Total energy (for Hydrogen and H2 like Atoms): The total energy of the electron in the mth stationary states of the hydrogen. An atom of the hydrogenlike atom of atomic number Z is given by
`E = - ((me^4)/(8ε_0^2h^2)) Z^2/n^2 = - ((me^4)/(8ε_0^2ch^3)) ch Z^2/n^2`
= `- R ch Z^2/n^2`
= `- 13.6 Z^2/n^2 eV`
For a He-nucleus Z = 2, and for ground state n = 1.
Thus, the ground state energy of a He-atom.
`E_n = - 13.6 Z^2/n^2 eV`
= `- 13.6 2^2/1^2 eV`
= – 54.4 eV
Thus, the ground state will have two electrons each of energy E and the total ground state energy would be – (4 × 13.6) eV = – 54.4 eV
APPEARS IN
RELATED QUESTIONS
Thorium 90Th232 is disintegrated into lead 82Pb200. Find the number of α and β particles emitted in disintegration.
In the ground state of ______ electrons are in stable equilibrium, while in ______ electrons always experience a net force.
An atom has a nearly continuous mass distribution in a ______ but has a highly non-uniform mass distribution in ______.
The positively charged part of the atom possesses most of the mass in ______.
Answer the following question, which help you understand the difference between Thomson’s model and Rutherford’s model better.
Is the probability of backward scattering (i.e., scattering of α-particles at angles greater than 90°) predicted by Thomson’s model much less, about the same, or much greater than that predicted by Rutherford’s model?
Answer the following question, which help you understand the difference between Thomson’s model and Rutherford’s model better.
In which model is it completely wrong to ignore multiple scattering for the calculation of average angle of scattering of α-particles by a thin foil?
Alpha particles used in Geiger-Marsden experiment were obtained from ______.
In Geiger-Marsden experiment prediction was that ______.
The model that best explains the results of Geiger-Marsden experiment is ______.
An automobile moves on a road with a speed of 54 km h−1. The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg m2. If the vehicle is brought to rest in l 5s, the magnitude of average torque transmitted by its brakes to the wheel is:
In 88 Ra226 nucleus, there are
A narrow beam of protons, each having 4.1 MeV energy is approaching a sheet of lead (Z = 82). Calculate:
- the speed of a proton in the beam, and
- the distance of its closest approach
If λa, λb and λc represent the Kα, Kβ and Lα transition wavelengths in a hydrogen atom, respectively. Then which of the following is correct?
The shortest wavelength of the Brackett series of a hydrogen like atom of atomic number Z is same as the shortest wavelength of the Balmer series of hydrogen atom, then the value of Z is ______.
Choose the correct option from the following options given below:
How is the size of a nucleus found experimentally? Write the relation between the radius and mass number of a nucleus.
Radius of the 1st orbit of hydrogen atom is r0. What will be the radius of the 4th orbit?
During Rutherford’s gold foil experiment, it was observed that most of the α-particles did not deflect. However, some showed a deflection of 180°.
What hypothesis was made to justify the deflection of α-particle by 180°?
