Problem 123 - A Complete Resource Book in Chemistry for JEE Main

Question

Which relation is/are correct? (a) \(1 \mathrm{Ci}=3.7 \times 10^{10} \mathrm{~Bq}\) (b) \(1 \mathrm{Ci}=2.8 \mathrm{v} 10^{4} \mathrm{Rd}\) (c) \(1 \mathrm{~Bq}=1 \mathrm{dps}\). (d) \(1 \mathrm{~Bq}=10^{6} \mathrm{Rd}\)

Step-by-Step Solution

Answer

Relations (a) and (c) are correct.

Step 1: Analyze Relation (a)

Start by understanding the relation given as \(1 \mathrm{Ci}=3.7 \times 10^{10} \mathrm{Bq}\). A Curie (Ci) is defined as \(3.7 \times 10^{10}\) disintegrations per second, which makes this relation true as 1 Becquerel (Bq) is defined as 1 disintegration per second.

Step 2: Analyze Relation (b)

Examine the relation \(1 \mathrm{Ci}=2.8 \times 10^{4} \mathrm{Rd}\). The unit Roentgen (Rd) is a measure of exposure, not directly related to activity which is measured in curies or becquerels. Hence, this relation is incorrect as the conversion does not make sense in physical terms.

Step 3: Analyze Relation (c)

Look at \(1 \mathrm{~Bq}=1 \mathrm{dps}\). This statement is true because 1 Becquerel is exactly defined as 1 disintegration per second (dps).

Step 4: Analyze Relation (d)

Consider \(1 \mathrm{~Bq}=10^{6} \mathrm{Rd}\). Similar to step 2, Becquerel deals with radioactive activity, while Roentgen is about radiation exposure; these units measure different things, making this relation incorrect.

Key Concepts

Curie (Ci)

The Curie, abbreviated Ci, is a unit of radioactivity named after Marie Curie, the pioneering scientist who conducted groundbreaking research on radiation. It is used to measure the amount of radioactivity in a substance. A Curie is a substantial amount of activity, defined as exactly 3.7 x 10^10 disintegrations per second. This means that in one second, a sample with the activity of 1 Ci undergoes 37 billion atomic decay events. Such a high number indicates why it's mostly used to express activity of large amounts of radioactive material, typically found in nuclear medicine or industrial applications.

Understanding Curie measurements can be important for safety, proper handling, and storage of radioactive substances. In smaller scales, the milliCurie (mCi) or microCurie (μCi) may be used to represent lesser quantities, with 1 mCi representing 1/1000 of a Ci and 1 μCi representing 1/1,000,000 of a Ci.

Becquerel (Bq)

The Becquerel, abbreviated Bq, is the SI unit of radioactivity. It is named after Henri Becquerel, who discovered radioactivity. Unlike the Curie, the Becquerel measures radioactivity as one disintegration per second. Hence, 1 Bq is far less than 1 Ci as it only accounts for one decay event each second. The Bq is suitable for use when measuring radioactivity in more controlled or smaller scenarios, like laboratory samples or environmental measurements.

The difference between Bq and Ci is illustrative of the significance of activity being measured. For example, laboratory experiments often report radioactivity in Becquerels for greater precision and because the levels often reflect manageable, smaller-scale samples. The conversion between Ci and Bq is significant: 1 Ci equals 3.7 x 10^10 Bq, showing the preferred unit depends on the level of radioactive material one deals with.

Roentgen (Rd)

The Roentgen, abbreviated Rd, is a unit of measurement related to radiation rather than radioactivity. It measures the exposure of X-rays or gamma rays in the air. Thus, the Roentgen is not directly related to the activity of a substance represented by units like Ci or Bq. While Roentgen measures exposure concerning ionization in the air, Becquerel and Curie measure the rate of radioactive decay or disintegration events.

Understanding this differences helps in correctly applying these terms. While news reports or health advisories may refer to Roentgen when talking about the amount of radiation exposure or potential health effects, scientists would use Bq or Ci to describe how active a radioactive material remains. Since these units serve different purposes, their conversions do not hold physical sense directly and are not typically used interchangeably in scientific context.