Question

For a hydrogen- like atom, classify these electron transitions by whether they result in the absorption or emission of light:

Answer 1

When an electron transit from lower level to higher level it emits energy

When an electron transit from higher level from a lower level it absorbs energy

n=3 to n=5,  : absorption

n=1 to n=3,  : absorption

n=3 to n=2,  : emission

n=2 to n=1 : emission

the highest energy means highest wave number

wave number = Rh (1/ n1^2 - 1/n2^2)

Rh = 1.1 X 10^7 m^-1

1) n=3 to n=5

wavenumber = Rh ( 1/ 9 - 1/ 25) = 0.071 Rh

2) n=1 to n=3

wavenumber = Rh ( 1- 1/9 ) = 0.89 Rh

3) n=3 to n=2

wavenumber = Rh ( 1/4 - 1/9) = 0.139 Rh

4) n=2 to n=1

wavenumber = Rh ( 1- 1/4) = 0.75 Rh

Thus for 2) n=1 to n=3 energy will be maximum

Answer 2

The classification of transitions are as follows:

The transition from n = 3 energy level to n = 5 energy level is an absorption process.

The transition from n = 1 energy level to n = 3 energy level is an absorption process.

The transition from n = 3 energy level to n = 2 energy level is an emission process.

The transition from n = 2 energy level to n = 1 energy level is an emission process.

The transition from n = 1 energy level to n = 3 energy level has the greatest change in energy.

Further Explanation:

Concept:

An electronic transition is a process that occurs when an electron undergoes emission or absorption from one energy level to another energy level.

When an electron undergoes transition from lower energy level to the higher energy level then it requires energy to complete the process. This transition is an absorption process.

When an electron undergoes transition from higher energy level to lower energy level then it emits energy to complete the process. This transition is an emission process.

The formula to calculate the difference between two energy levels of the hydrogen atom is,

$\Delta E = {R_{\text{H}}}\left( {\frac{1}{{{{\left( {{{\text{n}}_{\text{i}}}} \right)}^2}}} - \frac{1}{{{{\left( {{{\text{n}}_{\text{f}}}} \right)}^2}}}} \right)$

Where,

$\Delta E$ is the energy difference between two energy levels.

${R_{\text{H}}}$ is a Rydberg constant.

${{\text{n}}_{\text{i}}}$ is the initial energy level of transition.

${{\text{n}}_{\text{f}}}$ is the final energy level of transition.

Solution:

Part A: Classification of transitions

1. In this transition, electron goes from lower energy level (n = 3) to higher energy level (n = 5), therefore it needs to absorb the energy. Hence, this transition is classified as an absorption process.

2.  In this transition, electron goes from lower energy level (n = 1) to higher energy level (n = 3), therefore it needs to absorb the energy. Hence, this transition is classified as an absorption process.

3.  In this transition, electron goes from higher energy level (n = 3) to lower energy level (n = 2), therefore it needs to emit the energy. Hence, this transition is classified as an emission process.

4. In this transition, electron goes from higher energy level (n = 2) to lower energy level (n = 1), therefore it needs to emit the energy. Hence, this transition is classified as an emission process.

Part B: Finding the transition of greatest energy difference.

1.  In this transition, initial energy level is n = 3 and the final energy level is n = 5, the difference in energy is calculated as follows:

$\begin{aligned}\Delta E&= {R_{\text{H}}}\left( {\frac{1}{{{{\left( {{{\text{n}}_{\text{i}}}} \right)}^2}}} - \frac{1}{{{{\left( {{{\text{n}}_{\text{f}}}} \right)}^2}}}} \right) \hfill \\&= {R_{\text{H}}}\left( {\frac{1}{{{{\left( {\text{3}} \right)}^2}}} - \frac{1}{{{{\left( {\text{5}} \right)}^2}}}} \right)\hfill\\&= 0.071{R_{\text{H}}} \hfill\\\end{aligned}$

2.  In this transition, initial energy level is n = 1 and final energy level is n = 3, the difference in energy is calculated as follows:

$\begin{aligned}\Delta E&= {R_{\text{H}}}\left( {\frac{1}{{{{\left( {{{\text{n}}_{\text{i}}}} \right)}^2}}} - \frac{1}{{{{\left( {{{\text{n}}_{\text{f}}}} \right)}^2}}}} \right) \hfill \\&= {R_{\text{H}}}\left( {\frac{1}{{{{\left( {\text{1}} \right)}^2}}} - \frac{1}{{{{\left( {\text{3}} \right)}^2}}}} \right) \hfill \\&= 0.88{R_{\text{H}}} \hfill \\ \end{aligned}$

3.  In this transition, initial energy level is n = 3 and final energy level is n = 2, the difference in energy is calculated as follows:

$\begin{aligned}\Delta E&= {R_{\text{H}}}\left( {\frac{1}{{{{\left( {{{\text{n}}_{\text{i}}}} \right)}^2}}} - \frac{1}{{{{\left( {{{\text{n}}_{\text{f}}}} \right)}^2}}}} \right) \hfill \\&= {R_{\text{H}}}\left( {\frac{1}{{{{\left( {\text{3}} \right)}^2}}} - \frac{1}{{{{\left( {\text{2}} \right)}^2}}}} \right) \hfill \\&=- 0.139{R_{\text{H}}} \hfill \\ \end{aligned}$

4.  In this transition, initial energy level is n = 2 and final energy level is n = 1, the difference in energy is calculated as follows:

$\begin{aligned}\Delta E&= {R_{\text{H}}}\left( {\frac{1}{{{{\left( {{{\text{n}}_{\text{i}}}} \right)}^2}}} - \frac{1}{{{{\left( {{{\text{n}}_{\text{f}}}} \right)}^2}}}} \right) \hfill \\&= {R_{\text{H}}}\left( {\frac{1}{{{{\left( {\text{2}} \right)}^2}}} - \frac{1}{{{{\left( {\text{1}} \right)}^2}}}} \right) \hfill \\&=- 0.75{R_{\text{H}}} \hfill \\ \end{aligned}$

Hence the transition which is associated with the greatest energy change is a transition from energy level n = 1 to n = 3.

Learn more:

1. Identify oxidation numbers: brainly.com/question/2086855

2. Calculation of volume of gas: brainly.com/question/3636135

Answer details:

Grade: Senior School

Subject: Chemistry

Chapter: Atomic structure

Keywords: Transition, energy difference, greatest, hydrogen, absorption, emission.