Answer :
Answer:
For an electron to move from a lower energy level to a higher energy , that electron needs to absorb energy sufficient enough to excite it to make the transition. Hence it is an absorption process. The required energy of transition E = 2.665 x 10⁻²⁰J
Explanation:
Using the Rydberg's equation we can calculate the wavelength of the photon of energy transition as follows:
1/λ = R . (1/nf² - 1/ni²)
where
λ is the required wavelength of the photon needed to be absorbed to excite the electron to transit from level 5 to 6.
(Note that for the electron to transit to from energy level 5 to 6, the photon would have to fall from level 6 to 5 in order to emit the required energy to excite the electron)
R is the Rydberg's constant 1.097 x 10⁷ m⁻¹
nf is the final level of the photon
ni is the initial level of the photon
1/λ = 1.097 x 10⁷ m⁻¹ (1/5² - 1/6²)
1/λ = 1.3407 x 10⁵ m⁻¹
λ = 7.458 x 10⁻⁶ m
This implies that that is the wavelength of the photon required to excite the electron to transit from energy level 5 to 6. Using the equation below, we can calculate the energy of transition as
E = h.c/λ
where
E is the required energy of transition
h is the Planck's constant (6.626 x 10⁻³⁴ Js)
c is the speed of light (3 x 10⁸ms⁻¹)
λ is the wavelength calculated above
E = 6.626 x 10⁻³⁴ Js x 3 x 10⁸ms⁻¹/ 7.458 x 10⁻⁶ m
E = 2.665 x 10⁻²⁰J
1. The energy for the transition of an electron in a hydrogen atom from one level to another (5 to 6) is equal to
2. The transition of an electron in a hydrogen atom from the n = 5 level to the n = 6 level is an absorption (A) process because heat energy is absorbed.
Given the following data:
- Initial transition = 5
- Final transition = 6
Scientific data:
Atomic number of hydrogen = 1
To calculate the energy for the transition of an electron in a hydrogen atom from one level to another:
Mathematically, the energy of an electron in nth orbit is given by the formula:
[tex]E_n = -13.6\frac{Z^2}{n^2}[/tex]
Where:
- Z is the atomic number.
- n is the energy level or number of orbit.
When n = 5:
[tex]E_5 = -13.6 \times \frac{1^2}{5^2}\\\\E_5 =\frac{-13.6}{25} \\\\E_5 =-0.544\;eV[/tex]
When n = 6:
[tex]E_6 = -13.6 \times \frac{1^2}{6^2}\\\\E_6 =\frac{-13.6}{36} \\\\E_6 =-0.378\;eV[/tex]
Next, we would calculate the energy required for this transition:
[tex]E = E_6 - E_5\\\\E=-0.378-(-0.544)\\\\E=-0.378+0.544[/tex]
Energy = 0.166 eV.
To convert the value in eV to Joules.
Note: 1 eV = [tex]1.60218 \times 10^{-19}[/tex] Joules
[tex]Energy = 0.166 \times 1.60218 \times 10^{-19}\\\\Energy = 2.66 \times 10^{-20}\;Joules[/tex]
In conclusion, the transition of an electron in a hydrogen atom from the n = 5 level to the n = 6 level is an absorption (A) process because heat energy is absorbed.
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