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) \(1 \mathrm{~Bq}=1\) dps. (d) \(1 \mathrm{~Bq}=10^{6} \mathrm{Rd}\)

Step-by-Step Solution

Answer

Relations (a), (b), and (c) are correct.

Step 1: Understanding the Problem

We need to identify which of the given relationships about the units Curie (Ci), Becquerel (Bq), and Rutherford (Rd) are correct. Both Curie and Becquerel are units of radioactivity, with Ci being an older unit and Bq being the current SI unit.

Step 1: Verify Relation of Curie to Becquerel

Check the conversion given for Curie and Becquerel: A Curie is defined as the amount of radioactivity corresponding to 3.7 × 10^{10} disintegrations per second (dps), which is equivalent to Becquerel units. Therefore, \[1 \mathrm{Ci} = 3.7 \times 10^{10} \mathrm{~Bq} \]This statement (a) is correct.

Step 2: Check Conversion for Curie to Rutherford

Now, look at the conversion from Curie to Rutherford:The Rutherford (Rd) was an older unit defined as 10^6 disintegrations per second. Since 1 Ci = 3.7 × 10^{10} dps, converting to Rutherfords:\[1 \mathrm{Ci} = \frac{3.7 \times 10^{10}}{10^6} \mathrm{Rd} \]This simplifies to:\[1 \mathrm{Ci} = 3.7 \times 10^{4} \mathrm{Rd}\]Thus, statement (b) is also correct.

Step 3: Examine Becquerel Definition

Consider the definition of Becquerel, which represents one disintegration per second. Hence, \[1 \mathrm{~Bq} = 1 \text{ dps}\]This makes statement (c) correct.

Step 4: Check Becquerel to Rutherford Conversion

Finally, examine the conversion from Becquerel to Rutherfords:Since \(1 \mathrm{Rd} = 10^6 \mathrm{~Bq}\), the correct conversion is \[1 \mathrm{~Bq} = \frac{1}{10^6} \mathrm{Rd}\]This invalidates statement (d), because it is given incorrectly as \(1 \mathrm{~Bq} = 10^6 \mathrm{Rd}\).

Key Concepts

Curie to Becquerel Conversion

When dealing with radioactivity, it's important to understand the relationship between different units. Curie (Ci) and Becquerel (Bq) are two primary units used to measure radioactivity. Curie is an older, non-SI unit, while Becquerel is the standard SI unit.
A Curie is defined based on the decay rate of 1 gram of radium-226, which amounts to approximately 3.7 × 10^{10} disintegrations per second. Consequently, the conversion from Curie to Becquerel is straightforward:

• 1 Ci = 3.7 × 10^{10} Bq

This means that one Curie represents a vast number of disintegrations per second compared to one Becquerel, as 1 Bq simply equals one disintegration per second.
Understanding this conversion is crucial for comparing historical data with current scientific studies, as the radioactivity of a sample is often documented in either or both of these units.

Rutherford Units

The Rutherford (Rd) is a lesser-known unit of radioactivity named after the famous physicist Ernest Rutherford. Although it's not commonly used today, understanding it can provide a historical context for how radioactivity was measured in the past.
A Rutherford is defined as 10^6 disintegrations per second. To convert from Curie to Rutherford, you need to consider the number of disintegrations that 1 Ci represents:

• 1 Ci = 3.7 × 10^{10} disintegrations per second

Hence, converting to Rutherfords:

• 1 Ci = 3.7 × 10^{10} Bq / 10^6 Rd
• 1 Ci = 3.7 × 10^{4} Rd

The relation highlights that a Curie represents a large multiple of Rutherfords, underscoring the powerful level of activity a Curie denotes relative to the older Rutherford unit. Understanding these conversions aids in interpreting diverse scientific literature and data.

Becquerel Definition

The Becquerel (Bq) is the SI unit for measuring radioactivity. This unit is named after Henri Becquerel, the scientist credited with discovering radioactivity. Its definition is simple yet critically important: one Becquerel equals one disintegration per second.
Expressed mathematically:

• 1 Bq = 1 disintegration per second (dps)

The straightforward nature of this definition makes it an ideal unit for international use and standardization of radioactivity measurements.
Additionally, its simplicity provides a clear and direct way to communicate how much radioactive decay is occurring in a sample. Whether you are navigating scientific research or learning about radioactivity, appreciating this basic definition helps in understanding more complex topics in the field.