Question

Calculate the wavelength corresponding to a transition of electrons from the n = 6 energy level to the n = 3 level in a B4+ ion. (Use En= -R(z²/n²))

Using your answer from the question above what is the speed that an electron would need to travel in order to display the same wavelength?

Answer 1

Using the relation:

E_n= (-2.18 x 10^-18 J/mol) Z²/n²

Here Z is the atomic number.

For the boron ion B⁴⁺, Z = 5

Putting values in the equation to calculate the energy of transition, we get:

E₆ - E₃ = (-2.18 x 10^-18 ) (5²/6² - 5²/3²) = 82.916 J/mol

Using the Planck's equation:

E = h*(c/), where h is planck's constant = 6.62*10^-34 m².kg/s, c = speed of light = 3*10⁸ m/s,

Putting values and calculating we get:

= 1.4427*10^-3 m

For calculating the speed of electron with this much energy, we use the following relation:

E = 0.5*m*v2

Here, m is mass of electron, and v is its velocity

Putting values, we get:

82.916 J = 0.5 * (9.0 * 10^-31 kg) * v²

Solve this to calculate v.