Wave Optics

Question

Which state of the triply ionized Be⁺⁺⁺ has the same orbital radius as that of the ground state of hydrogen? Compare the energies of two states.

Solution

Radius of nth orbit is given by,

r = \frac{n^{2} h^{2}}{4 π^{2} {mKZe}^{2}}

i . e ., r \propto \frac{n^{2}}{Z}

For hydrogen, Z = 1, n = 1 in ground state.

∴

\frac{n^{2}}{Z} = \frac{1^{2}}{1} = 1

For Berylium, Z = 4, as orbital radius is same,

\frac{n^{2}}{Z} = 1

∴

n^{2} = 1 \times Z = 1 \times 4 = 4 n = \sqrt{4} = 2

Hence n = 2.

Thus, second level of triply ionised Be⁺⁺⁺ has same radius as the ground state of hydrogen.

Now energy of electron in nth orbit is given by,

E = - \frac{2 π^{2} {mK}^{2} Z^{2} e^{4}}{n^{2} h^{2}}

∴

E \propto \frac{Z^{2}}{n^{2}}

\frac{E_{(Be)}}{E_{H}} = \frac{{[Z^{2} / n^{2}]}_{Be}}{[Z^{2} / n^{2}]} = \frac{16 / 4}{1 / 1} = 4

Therefore, energy of ionized Be is greater than the energy of hydrogen in the ground state.

Some More Questions From Wave Optics Chapter

In the ground state of electrons are in stable equilibrium, while in electrons always experience a net force. (Thomson's model/Rutherford's model).

A classical atom based on __________ is doomed to collapse. (Thomson's model/Rutherford's model)

An atom has a nearly continuous mass distribution in a ___ but has a highly non-uniform mass distribution in (Thomson's model/Rutherford's model)

The positively charged part of the atom possesses most of the mass in ___________ (Rutherford's model/both the models).

Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?

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Wave Optics

Which state of the triply ionized Be⁺⁺⁺ has the same orbital radius as that of the ground state of hydrogen? Compare the energies of two states.

Some More Questions From Wave Optics Chapter

In the ground state of electrons are in stable equilibrium, while in electrons always experience a net force. (Thomson's model/Rutherford's model).

A classical atom based on __________ is doomed to collapse. (Thomson's model/Rutherford's model)

An atom has a nearly continuous mass distribution in a ___ but has a highly non-uniform mass distribution in (Thomson's model/Rutherford's model)

The positively charged part of the atom possesses most of the mass in ___________ (Rutherford's model/both the models).

Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Wave Optics

Which state of the triply ionized Be+++ has the same orbital radius as that of the ground state of hydrogen? Compare the energies of two states.

Some More Questions From Wave Optics Chapter

In the ground state of __________ electrons are in stable equilibrium, while in __________ electrons always experience a net force. (Thomson's model/Rutherford's model).

A classical atom based on __________ is doomed to collapse. (Thomson's model/Rutherford's model)

An atom has a nearly continuous mass distribution in a _____________ but has a highly non-uniform mass distribution in __________ (Thomson's model/Rutherford's model)

The positively charged part of the atom possesses most of the mass in ___________ (Rutherford's model/both the models).

Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Which state of the triply ionized Be⁺⁺⁺ has the same orbital radius as that of the ground state of hydrogen? Compare the energies of two states.

In the ground state of electrons are in stable equilibrium, while in electrons always experience a net force. (Thomson's model/Rutherford's model).

An atom has a nearly continuous mass distribution in a ___ but has a highly non-uniform mass distribution in (Thomson's model/Rutherford's model)