JEE Main 2024 — Structure Of Atom Question with Solution

The definition of the candela involves a source emitting monochromatic radiation of a specific frequency and having a precise radiant intensity in a given direction. The candela is thereby defined based on both the frequency of the monochromatic light and its radiant intensity in watts per steradian. According to the given statement, we are dealing with a frequency identified as '$$A$$' $$\times 10^{12}$$ hertz and a radiant intensity specified as $$\frac{1}{B}$$ watt per steradian. However, there seems to be a small confusion in how the values are represented in the question. The correct interpretation and formulation based on the International System of Units (SI) are as follows:

The frequency of the monochromatic radiation that is used in defining the candela is 540 THz (tera hertz), so the value of $$A$$ should be 540. The specific radiant intensity mentioned relates to how the candela is defined in terms of a source's power output in a particular direction within a given frequency. The value that corresponds to the efficiency of human visual perception at this frequency is approximately 683 lumens per watt. Therefore, the number 683 is involved in specifying how many lumens correspond to a power of one watt of monochromatic light at 540 THz.

Given this context, the correct answer derives from understanding that:

• '$$A$$' represents the frequency in THz, which is 540 for the definition of the candela.
• '$$B$$' refers to the conversion factor or the luminous efficacy in lumens per watt at this frequency, which is 683 lumens per watt, not its reciprocal.

Therefore, the correct values for '$$A$$' and '$$B$$' are 540 and 683, respectively, making Option C the correct answer.