MCQEasyJEE 2024SI System & Derived Units

JEE Physics 2024 Question with Solution

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency A×1012hertzA \times 10^{12} \, \text{hertz} and that has a radiant intensity in that direction of 1B\frac{1}{B} watt per steradian. ’AA’ and ’BB’ are respectively:

  • A

    540540 and 11

  • B

    540540 and 683683

  • C

    450450 and 11

  • D

    450450 and 683683

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given: The candela is defined using monochromatic radiation of frequency A×1012hertzA \times 10^{12} \, \text{hertz} and radiant intensity 1B\frac{1}{B} watt per steradian.

Find: The values of AA and BB.

From the SI definition, candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency

540×1012hertz540 \times 10^{12} \, \text{hertz}

and that has a radiant intensity in that direction of

1683watt per steradian\frac{1}{683} \, \text{watt per steradian}

Comparing with the given form:

A×1012hertzA \times 10^{12} \, \text{hertz}

and

1Bwatt per steradian\frac{1}{B} \, \text{watt per steradian}

we get

A=540A = 540

and

B=683B = 683

Using the SI Definition of Candela

Given: A question based on the SI base unit candela.

Find: Which option matches the standard definition.

The standard definition states that candela corresponds to monochromatic radiation of frequency 540×1012hertz540 \times 10^{12} \, \text{hertz}.

It also states that the radiant intensity in that direction is 1683watt per steradian\frac{1}{683} \, \text{watt per steradian}.

Therefore, the required pair is 540540 and 683683. The correct option is B.

Common mistakes

  • Confusing the frequency value with 450×1012hertz450 \times 10^{12} \, \text{hertz}. This is incorrect because the SI definition of candela specifically uses 540×1012hertz540 \times 10^{12} \, \text{hertz}. Always recall the exact standard definition.

  • Taking the radiant intensity as 11\frac{1}{1} instead of 1683\frac{1}{683} watt per steradian. This is wrong because 683683 is part of the fixed SI definition. Match the denominator carefully.

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