Respuesta :
Answer : The energy of photon = [tex]21.369\times 10^{-19}J[/tex]
Solution : Given,
Final energy level = 1
Initial energy level = 7
Formula used :
[tex]\frac{1}{\lambda}=R[ \frac{1}{n^2_{final}}- \frac{1}{n^2_{initial}}][/tex] ..........(1)
where,
[tex]\lambda[/tex] = wavelength
R = Rydberg's constant = 1.0974 [tex]\times 10^7m^{-1}[/tex]
[tex]n_{final}[/tex] = final energy level
[tex]n_{initial}[/tex] = initial energy level
Now put all the given values in above formula (1), we get the value of wavelength.
[tex]\frac{1}{\lambda}=1.0974\times 10^7m^{-1} [\frac{1}{1^2}- \frac{1}{7^2}][/tex] = [tex]1.0750\times 10^7m^{-1}[/tex]
[tex]\lambda=0.9302\times 10^{-7}m[/tex]
Now we have to calculate the energy of photon by using formula,
[tex]E=\frac{h\times c}{\lambda}[/tex]
where,
E = energy
h = planck's constant = [tex]6.626\times 10^{-7}Js[/tex]
c = speed of light = [tex]3\times 10^8m/s[/tex]
[tex]\lambda[/tex] = wavelength
put all the values in this formula, we get the energy of photon.
[tex]E=\frac{6.626\times 10^{-7}Js\times 3\times 10^8m/s}{0.9302\times 10^{-7}m}[/tex] = [tex]21.369\times 10^{-19}J[/tex]
