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: Understanding the Question:
The threshold wavelength is the longest wavelength of light that can still knock electrons out of a metal. We must list the four metals from the largest threshold wavelength to the smallest.

Step 2: Key Formula or Approach:
The work function is the minimum energy needed to free an electron. It is linked to the threshold wavelength by \[ \Phi = \frac{hc}{\lambda_0} \quad \Rightarrow \quad \lambda_0 = \frac{hc}{\Phi} \] Here h and c are constants, so \(\lambda_0\) is inversely proportional to \(\Phi\).

Step 3: Decide the Order:
A larger work function gives a smaller threshold wavelength. So the largest threshold wavelength belongs to the smallest work function.
Work functions in increasing order: Cs (2.14 eV) < K (2.3 eV) < Na (2.75 eV) < Ca (3.2 eV).
So threshold wavelengths in decreasing order: Cs > K > Na > Ca, which is C, A, B, D.

Step 4: Checking Each Option:
Option 1 (A, B, C, D) is K, Na, Cs, Ca. Cs has the smallest work function, so it cannot come third. Wrong.
Option 2 (D, C, B, A) puts Ca first, but Ca has the largest work function and the shortest threshold wavelength. Wrong.
Option 3 (C, A, D, B) puts Ca before Na, but Na has the smaller work function. Wrong.
Option 4 (C, A, B, D) matches our order. Correct.

Final Answer:
The order of decreasing threshold wavelength is Cs, K, Na, Ca, that is C, A, B, D. This is option 4. \[ \boxed{4} \]