What is the energy
requirement of another energy
level from the energy level of -
3.7eV, if wavelength is 2.1 x 10-7
m?
[take c = 3.0 x 108m/s, 1eV = 1.6
x 10-19J, h= 6.6 x 10-34]
A. 5eV
B. 6eV
C. 10eV
D. 8eV
To find the energy requirement of another energy level, we can use the formula:
E = hc / λ
where E is the energy, h is the Planck's constant, c is the speed of light, and λ is the wavelength.
Given:
λ = 2.1 x 10^-7 m
c = 3.0 x 10^8 m/s
Plugging in the values:
E = (6.6 x 10^-34 J s) * (3.0 x 10^8 m/s) / (2.1 x 10^-7 m)
E = (1.98 x 10^-25 J m) / (2.1 x 10^-7 m)
E = 9.42 x 10^-19 J
To convert this to electron volts (eV), we divide by 1.6 x 10^-19 J/eV:
E = (9.42 x 10^-19 J) / (1.6 x 10^-19 J/eV)
E = 5.89 eV
Therefore, the energy requirement of another energy level from the energy level of -3.7 eV with a wavelength of 2.1 x 10^-7 m is approximately 5.89 eV.
The closest answer choice is A. 5eV.
To find the energy requirement of another energy level, we can use the equation:
E = hc/λ
where:
E = energy
h = Planck's constant (6.6 x 10^-34 J·s)
c = speed of light (3.0 x 10^8 m/s)
λ = wavelength
Let's plug in the given values:
E = (6.6 x 10^-34 J·s) * (3.0 x 10^8 m/s) / (2.1 x 10^-7 m)
Calculating this expression:
E = (19.8 x 10^-26 J·m) / (2.1 x 10^-7 m)
E = 9.42857143 x 10^-19 J
Now, let's convert this energy to electron-volts (eV):
1 eV = 1.6 x 10^-19 J
E = (9.42857143 x 10^-19 J) / (1.6 x 10^-19 J/eV)
E ≈ 5.89 eV
Therefore, the energy requirement of another energy level is approximately 5.89 eV. Thus, the correct answer is not listed among the options provided.