Answer:
a) 1.866 × 10 ⁻¹⁹ J b) 3.685 × 10⁻¹⁹ J
Explanation:
the constants involved are
h ( Planck constant) = 6.626 × 10⁻³⁴ m² kg/s
Me of electron = 9.109 × 10 ⁻³¹ kg
speed of light = 3.0 × 10 ⁸ m/s
a) the Ek ( kinetic energy of the dislodged electron) = 0.5 mu²
Ek = 0.5 × 9.109 × 10⁻³¹ × ( 6.40 × 10⁵ )² = 1.866 × 10 ⁻¹⁹ J
b) Φ ( minimum energy needed to dislodge the electron ) can be calculated by this formula
hv = Φ + Ek
where Ek = 1.866 × 10 ⁻¹⁹ J
v ( threshold frequency ) = c / λ where c is the speed of light and λ is the wavelength of light = 358.1 nm = 3.581 × 10⁻⁷ m
v = ( 3.0 × 10 ⁸ m/s ) / (3.581 × 10⁻⁷ m ) = 8.378 × 10¹⁴ s⁻¹
hv = 6.626 × 10⁻³⁴ m² kg/s × 8.378 × 10¹⁴ s⁻¹ = 5.551 × 10⁻¹⁹ J
5.551 × 10⁻¹⁹ J = 1.866 × 10 ⁻¹⁹ J + Φ
Φ = 5.551 × 10⁻¹⁹ J - 1.866 × 10 ⁻¹⁹ J = 3.685 × 10⁻¹⁹ J
