Question

The longest wavelength of light that can be used for the ionisation of lithium atom (Li) in its ground state is x ×10⁻⁸ m. The value of x is ___________. (Nearest Integer).

(Given : Energy of the electron in the first shell of the hydrogen atom is −2.2 ×10⁻⁸ ⁻¹⁸J; h=6.63x10⁻³⁴ Js and c=3x10⁸ ms⁻¹)

Answer 1

The longest wavelength that can be used for the ionization of a lithium atom is calculated by converting the ionization energy to joules, and applying the relationship between energy, Planck's constant, and the speed of light to solve for the desired wavelength.

Step-by-step explanation:

The question is asking for the longest wavelength of light (λ) that can ionize a lithium atom from its ground state. To find this wavelength, we need to use the energy required for ionization and the relationship between energy (E), Planck's constant (h), and the speed of light (c). The energy required to ionize lithium is given as +54.4 eV and we can convert this to joules by multiplying by the conversion factor (1 eV = 1.602 × 10-19 J). Once we have the energy in joules, we can use the equation E = h*c/λ to solve for the wavelength.

Firstly, convert the ionization energy to joules:

E (in J) = 54.4 eV * 1.602 × 10-19 J/eV = 8.709 × 10-18 J

Now, apply the formula to find λ:

λ = (h*c)/E = (6.63 × 10-34 J·s * 3 × 108 m/s) / 8.709 × 10-18 J

To find x in λ = x × 10-8 m, we rearrange to get x:

x = λ / 10-8 = (6.63 × 10-34 * 3 × 108) / (8.709 × 10-18 * 10-8)

Calculating x, we obtain a value (which you will need to compute), and this will be the answer to the question, rounded to the nearest integer.