Question

Calculate and compare the energy of two radiations one with wavelength 800pm and other with 400pm

Answer 1

800pm = 8 A° (angstrom)
400pm = 4 A°
Energy of first radiation = 12400 ÷ 8 = 1550 eV
Energy of second radiation = 12400 ÷ 4 = 3100 eV

Answer 2

Let us consider a radiation having wavelength $\lambda$.

From Planck's quantum theory, we know that the energy of the radiation is h times wavelength .

Mathematically energy E = $h\nu$

But we know that $\nu=\frac{c}{\lambda}$.

Hence, energy E = $\frac{hc}{\lambda}$

Here, h is the planck constant and $\nu$ is the frequency of radiation.

c is the velocity of light.

We know that 1 pico metre = $10^{-12}\ m$

The wavelength of the first radiation is given as $\lambda_{1}\ =\ 800\ pm$

                                                                                           $=\ 800\times 10^{-12}\ m$

                                                                                           $=\ 8\times10^{-10}\ m$

The wavelength of the second radiation  $\lambda_{2}=\ 400\ pm$

                                                                        $=\ 400\times 10^{-12}\ m$

                                                                        $=\ 4\times 10^{-10}\ m$

The energy of the first radiation is calculated as -

                                       $E_{1}=\ \frac{hc}{\lambda_{1}}$

                                              $=\ \frac{6.63\times 10^{-34}\times 3\times 10^8} {8\times 10^{-10}}$

                                              $=\ 2.49\times 10^{-16}\ J$  [ans]

                                             

The energy of the second radiation is calculated as -

                                      $E_{2} =\ \frac{hc}{\lambda_{2}}$

                                            $=\frac{6.63\times 10^{-34}\times 3\times 10^8} {4\times 10^{-10}}$

                                            $=\ 4.98\times 10^{-16}\ J$    [ans]

From above, it is obvious that energy of 400 pm radiation is more as compared to energy of 800 pm radiation. It means energy is inversely proportional to wavelength.