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
With the help of a neat labelled diagram, describe the Geiger- Marsden experiment
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 average angle of deflection of α-particles by a thin gold foil predicted by Thomson’s model much less, about the same, or much greater than that predicted by Rutherford’s model?
The model that best explains the results of Geiger-Marsden experiment is ______.
The first line of Balmer series (Hα) in the spectrum of hydrogen is obtained when an electron of hydrogen atom goes from ______.
As compared to 12C atom, 14C atom has ______.
In a capillary tube, water rises by 1.2 mm. The height of water that will rise in another capillary tube having half the radius of the first is:
Which one of the following statements does not hold good when two balls of masses m1 and m2 undergo elastic collision?
O2 molecule consists of two oxygen atoms. In the molecule, nuclear force between the nuclei of the two atoms ______.
The energy of hydrogen atom in an orbit is −1.51 eV. What are the kinetic and potential energies of the electron in this orbit?
The electron in a hydrogen atom is typically found at a distance of about 5.3 × 10−11 m from the nucleus which has a diameter of about 1.0 × 10−15 m. Assuming the hydrogen atom to be a sphere of radius 5.3 × 10−11 m, what fraction of its volume is occupied by the nucleus?
According to Bohr model, magnetic field at centre (at the nucleus) of a hydrogen atom due to motion of electron in the ninth orbit is proportional to:
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 ______.
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°?
What was the purpose of the zinc sulphide fluorescent screen?
How does the size of the nucleus compare with the size of the atom?
What occupies most of the space in the atom in Rutherford’s nuclear model?
