Question

What are the possible wavelengths of light that could be emitted by a gas of hydrogen atoms in the third-excited (n = 4) state?

Answer 1

possible transactions :

n=4 --> n = 3
n=4 --> n = 2
n=4 --> n = 1

n=3 --> n = 2
n=3 --> n = 1

n=2 --> n = 1

wavelength emited photon,

1/lamda = R*(1/nf^2 - 1/ni^2)

we know, Rydburg constant, R = 1.097*10^7 m^-1

for transaction : n=4 --> n = 3

1/lamda = R*(1/nf^2 - 1/ni^2)

1/lamda = 1.097*10^7*(1/3^2 - 1/4^2)

lamda = 1.88*10^-6 m <<<<<<------------------Answer

for transaction : n=4 --> n = 2

1/lamda = R*(1/nf^2 - 1/ni^2)

1/lamda = 1.097*10^7*(1/2^2 - 1/4^2)

lamda = 4.87*10^-7 m <<<<<<------------------Answer

for transaction : n=4 --> n = 1

1/lamda = R*(1/nf^2 - 1/ni^2)

1/lamda = 1.097*10^7*(1/1^2 - 1/4^2)

lamda = 9.72*10^-8 m <<<<<<------------------Answer

for transaction : n=3 --> n = 2

1/lamda = R*(1/nf^2 - 1/ni^2)

1/lamda = 1.097*10^7*(1/2^2 - 1/3^2)

lamda = 6.56*10^-7 m <<<<<<------------------Answer

for transaction : n=3 --> n = 1

1/lamda = R*(1/nf^2 - 1/ni^2)

1/lamda = 1.097*10^7*(1/1^2 - 1/3^2)

lamda = 1.03*10^-7 m <<<<<<------------------Answer

for transaction : n=2 --> n = 1

1/lamda = R*(1/nf^2 - 1/ni^2)

1/lamda = 1.097*10^7*(1/1^2 - 1/2^2)

lamda = 1.22*10^-7 m <<<<<<------------------Answer