In the given radioactive disintegration series
`._(92)^(235)U rarr_(82)^(207)Pb`
Calculate difference between number of `alpha` and number of `beta` particles emitted in this series.

Answer

To solve the problem of calculating the difference between the number of alpha and beta particles emitted in the radioactive disintegration series from Uranium-235 (U-235) to Lead-207 (Pb-207), we can follow these steps:

### Step 1: Understand the decay process
In a radioactive decay series, an unstable nucleus emits particles to become more stable. In this case, U-235 (with atomic number 92) decays to Pb-207 (with atomic number 82).

### Step 2: Calculate the change in atomic mass and atomic number
- The mass number of U-235 is 235, and that of Pb-207 is 207.
- The change in mass number is:
\[ 235 - 207 = 28 \]
- The change in atomic number is:
\[ 92 - 82 = 10 \]

### Step 3: Determine the number of alpha particles emitted
Each alpha particle emission decreases the atomic mass by 4 and the atomic number by 2. To find the number of alpha particles emitted, we can use the formula:
\[ \text{Number of alpha particles} = \frac{\text{Change in mass number}}{4} \]
Substituting the values:
\[ \text{Number of alpha particles} = \frac{28}{4} = 7 \]

### Step 4: Determine the number of beta particles emitted
Each beta particle emission increases the atomic number by 1. Since the atomic number decreases by 10 (from 92 to 82), the number of beta particles emitted is equal to this decrease:
\[ \text{Number of beta particles} = 10 \]

### Step 5: Calculate the difference between alpha and beta particles
Now, we can find the difference between the number of alpha and beta particles emitted:
\[ \text{Difference} = \text{Number of alpha particles} - \text{Number of beta particles} \]
Substituting the values:
\[ \text{Difference} = 7 - 10 = -3 \]

### Final Answer
The difference between the number of alpha and beta particles emitted in this series is -3.

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