Question 49 of 62advanced🔧 ApplyNumerical3 marks

Following results are observed when sodium metal is irradiated with different wavelengths. Calculate (a) threshold wavelength and, (b) Planck’s constant. λ (nm) 500 450 400 v × 10⁻⁵ (cm s⁻¹) 2.55 4.35 5.35

(a)
Answer

Threshold wavelength (λ0\lambda_0) is approximately 540540 nm

(b)
Answer

Planck's constant (hh) is approximately 6.6×10−346.6 \times 10^{-34} J s

Explanation

Using Einstein's photoelectric equation hcλ=hcλ0+12mv2\frac{hc}{\lambda} = \frac{hc}{\lambda_0} + \frac{1}{2}mv^2, we can set up simultaneous equations using the given pairs of wavelengths and velocities. Note that the velocity values in the table are interpreted as v×105v \times 10^5 m/s (or v×107v \times 10^7 cm/s) to yield physically consistent results for Planck's constant. By subtracting the equations for different wavelengths, the threshold work function term cancels out, allowing us to solve for hh. Substituting hh back into one of the equations gives the threshold wavelength λ0\lambda_0.