Which of the following species gives shortest wavelength of radiation ...
Answer
Option B) H
Explanation
When an electron jumps from a higher energy level (n2) to a lower energy level (n1), it releases energy in the form of electromagnetic radiation. The energy of the radiation is given by the difference in energy levels using the equation:
E = hv = (hc)/λ
where E is the energy of the radiation, h is Planck's constant, v is the frequency of the radiation, c is the speed of light, and λ is the wavelength of the radiation.
The shortest wavelength of radiation will occur when the energy difference between the two levels is the largest. The energy difference between two energy levels is given by:
ΔE = (hcR)/n^2
where R is the Rydberg constant and n is the principal quantum number of the energy level.
Using this equation, we can see that the largest ΔE occurs when n2 = 2 and n1 = 1. Plugging in the values, we get:
ΔE = (hcR)/(2^2) - (hcR)/(1^2) = (3hcR)/4
Therefore, the species with the shortest wavelength of radiation will be the one with the highest value of R. The Rydberg constant depends on the atomic number of the species, and is given by:
R = 1.0974 x 10^7 m^-1
For hydrogen (H), the atomic number is 1, so the Rydberg constant is the highest among the given options. Therefore, hydrogen will emit radiation with the shortest wavelength when an electron jumps from n2 = 2 to n1 = 1.