What is the energy needed to raise an electron in the hydrogen atom from the second energy level to the third energy level?
A. \(1.52 \times 10^4 \, \text{J}\)
B. \(3.63 \times 10^{-19} \, \text{J}\)
C. \(2.18 \times 10^{-19} \, \text{J}\)
D. \(4.48 \times 10^{-9} \, \text{J}\)
E. \(3.03 \times 10^{-19} \, \text{J}\)
Answer (3)
3.03 ∗ 1 0 − 19 J is the energy needed to raise an electron in the hydrogen atom from the **second energy **level to the **third energy **level.
What are Energy Levels?
The electrons that surround an atom around the nucleus are located in regions called **"energy levels". **It represents the **3-D space **that surrounds the nucleus where the electrons are present. It is divided into **several energy levels **such as first energy level, second energy level and so on.
The level that is closest to the nucleus is the first energy level , then the **second **one is further away from it, then the **third **one is a little further away and so on. Each energy level has different number of electrons like first has 2 electrons , second has 8 , third has **8 **and so on. The electrons which are further away from the nucleus are called valence electrons .
For **given above **information,
E = -\t E o / n 2
where,
E o = 13.6 eV (1 eV = 1.602×10-19 Joules) and n = 1,2,3… and so on so that the ground state has energy E 1 = -13.6 eV and the second energy level (the first excited state) has energy E 2 = -13.6/4 eV = -3.4 eV.
So,
1eV = 1.602× 10^-^1^9 J
Energy difference can be calculated by -13.6eV ( 1/ n f 3 - 1/ n i 2 )
n f = Final energy; n i = Initial energy
1.88 eV is equals to x
So, x= 3.03* 10^-^1^9
Thus, 3.03 ∗ 1 0 − 19 J is the energy needed to raise an electron in the hydrogen atom from the **second energy **level to the **third energy **level.
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To calculate the energy needed to raise an electron in the hydrogen atom from the second energy level to the third energy level, we need to find the difference in energy between the two levels. The energy of an electron in the hydrogen atom can be calculated using the formula E = -13.6/n^2 eV, where n is the principal quantum number. So, the energy of the electron in the second energy level (n=2) is E₂ = -13.6/(2^2) = -3.4 eV, and the energy of the electron in the third energy level (n=3) is E₃ = -13.6/(3^2) = -1.5 eV.
The energy needed to raise the electron from the second energy level to the third energy level is the difference between these two energies: ΔE = E₃ - E₂ = -1.5 eV - (-3.4 eV) = 1.9 eV.
To convert this energy to joules, we can use the conversion factor 1 eV = 1.6 × 10^-19 J. So, the energy needed to raise the electron is 1.9 eV × 1.6 × 10^-19 J/eV = 3.04 x 10^-19 J.
The energy needed to raise an electron in a hydrogen atom from the second energy level to the third is approximately 3.03 x 10^-19 J. This was calculated by finding the energy at each level using the formula for the energy of an electron in a hydrogen atom. The calculation shows the energy difference between the levels when transitioning from n=2 to n=3.
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