The concentration of Ni in a new alloy is determined by neutron activation analysis. A 0.500-g sample of the alloy and a 1.00-g sample of a standard alloy that is 5.93% w/w Ni are irradiated with neutrons in a nuclear reactor. When irradiation is complete, the sample and the standard are allowed to cool and their gamma ray activities are measured. Given that the activity is 1020 cpm for the sample and 3540 cpm for the standard, determine the %w/w Ni in the alloy.
To determine the %w/w Ni in the alloy using the given information, we can follow these steps:
1. Calculate the specific activity of the standard alloy:
- Specific Activity = Activity / Mass
- Specific Activity = 3540 cpm / 1.00 g
2. Calculate the specific activity of the sample alloy:
- Specific Activity = 1020 cpm / 0.500 g
3. Divide the specific activity of the sample alloy by the specific activity of the standard alloy:
- Specific Activity (Sample) / Specific Activity (Standard) = (%w/w Ni in the sample) / (%w/w Ni in the standard)
4. Rearrange the equation to solve for the %w/w Ni in the sample:
- (%w/w Ni in the sample) = Specific Activity (Sample) / Specific Activity (Standard) * (%w/w Ni in the standard)
Now let's perform the calculations:
1. Specific Activity (Standard) = 3540 cpm / 1.00 g = 3540 cpm/g
2. Specific Activity (Sample) = 1020 cpm / 0.500 g = 2040 cpm/g
3. (%w/w Ni in the sample) / (%w/w Ni in the standard) = 2040 cpm/g / 3540 cpm/g
4. (%w/w Ni in the sample) = (2040 cpm/g / 3540 cpm/g) * 5.93% w/w
Calculating the result:
(%w/w Ni in the sample) = (2040 / 3540) * 5.93% w/w
(%w/w Ni in the sample) ≈ 3.425% w/w
Therefore, the concentration of Ni in the new alloy is approximately 3.425% w/w.