Question

Arrange the following photosensitive metals (work function given in brackets) according to their threshold wavelengths in decreasing order of their values.
A. K (\(\Phi\) = 2.3 eV)
B. Na (\(\Phi\) = 2.75 eV)
C. Cs (\(\Phi\) = 2.14 eV)
D. Ca (\(\Phi\) = 3.2 eV)

Choose the correct answer from the options given below:

• A. A, B, C, D
• B. D, C, B, A
• C. C, A, D, B
• D. C, A, B, D

Hint:

Threshold wavelength is inversely proportional to the work function. Smallest work function means longest wavelength.

Answer 1

The Correct Option is D

Step 1: Convert Each Work Function:
Use $\lambda_0 = \dfrac{1240 \text{ eV nm}}{\Phi}$, a handy form of $hc/\Phi$. I will find each wavelength in nm.

Step 2: Calculate:
Cs: 1240/2.14 = 579 nm.
K: 1240/2.3 = 539 nm.
Na: 1240/2.75 = 451 nm.
Ca: 1240/3.2 = 388 nm.

Step 3: Arrange:
Decreasing order of wavelength: 579 (Cs) > 539 (K) > 451 (Na) > 388 (Ca). In the letters of the question this is C, A, B, D.

Step 4: Match With the Options:
Only option 4 lists C, A, B, D in this order. Options 1 to 3 place at least one metal in the wrong position.

Final Answer:
\[\boxed{\text{C, A, B, D (option 4)}}\]