Question

Calculate the atomic number of hydrogen like species which can be ionized by an electron moving with a velocity, v = 6.56 106 m s-1

Answer 1

The atomic number is Z = 3

• Given, Velocity of the electron = 6.56 * 10^6 m/s.
• We know, for Hydrogen like species,    Velocity of an electron is calculated by formula :
• V = (Z/n) * 2.18 * 10^6    , where 2.18*10^ 6 is velocity of an electron in 1st orbit of hydrogen, Z is atomic number, n is orbital number.
• Now, by substituting the given data,   6.56 * 10^6 = (Z/n) 2.18 * 10^6
• Let Z = 1 first calculate the n for Hydrogen atom
• n = 2.18 / 6.56  = 0.332 ≈ 1  ( n is always a whole number)
• Now, for hydrogen like atom having velocity of electron = 6.56 * 10^6 m/s in orbital 1
• 6.56 * 10^6 = 2.18 * 10^6 ( Z /1)

• Z = 3.009  ≈ 3
• Therefore, the atomic number of hydrogen like species which can be ionized by an electron moving with a velocity, v = 6.56 106 m s-1 is 3