If the wavelength for an electron emitted from $$H^-$$ atom is $$3.3 \times 10^{-10}$$ m, then energy absorbed by the electron in its ground state compared to minimum energy required for its escape from the atom, is _____ times. [Given: $$h = 6.626 \times 10^{-34}$$ Js, Mass of electron $$= 9.1 \times 10^{-31}$$ kg]

We are given that an electron emitted from a hydrogen atom has a de Broglie wavelength of $$\lambda = 3.3 \times 10^{-10}$$ m. We need to find how many times the energy absorbed by the electron in the ground state is, compared to the minimum energy required for its escape (ionization energy).

The minimum energy required for the electron to escape from the hydrogen atom in the ground state is the ionization energy of hydrogen:

$$E_{min} = 13.6 \text{ eV} = 13.6 \times 1.6 \times 10^{-19} = 2.176 \times 10^{-18} \text{ J}$$

Now, let us find the kinetic energy of the emitted electron using its de Broglie wavelength. From the de Broglie relation $$\lambda = \frac{h}{mv}$$, the kinetic energy is:

$$KE = \frac{1}{2}mv^2 = \frac{h^2}{2m\lambda^2}$$

Substituting the given values:

$$KE = \frac{(6.626 \times 10^{-34})^2}{2 \times 9.1 \times 10^{-31} \times (3.3 \times 10^{-10})^2}$$

Computing the numerator: $$(6.626)^2 = 43.90$$, so the numerator is $$43.90 \times 10^{-68}$$.

Computing the denominator: $$2 \times 9.1 \times (3.3)^2 = 2 \times 9.1 \times 10.89 = 198.2$$, with units $$10^{-31} \times 10^{-20} = 10^{-51}$$, so the denominator is $$198.2 \times 10^{-51}$$.

$$KE = \frac{43.90 \times 10^{-68}}{198.2 \times 10^{-51}} = 0.2215 \times 10^{-17} = 2.215 \times 10^{-18} \text{ J}$$

By the photoelectric effect principle, the total energy absorbed by the electron equals the minimum escape energy plus the kinetic energy of the emitted electron:

$$E_{absorbed} = E_{min} + KE = 2.176 \times 10^{-18} + 2.215 \times 10^{-18} = 4.391 \times 10^{-18} \text{ J}$$

Now we find the ratio of energy absorbed to the minimum escape energy:

$$\frac{E_{absorbed}}{E_{min}} = \frac{4.391 \times 10^{-18}}{2.176 \times 10^{-18}} \approx 2.02 \approx 2$$

So the energy absorbed by the electron is approximately 2 times the minimum energy required for its escape from the atom.

Hence, the correct answer is 2.