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Chapter 29: Problem 21

Identify the daughter nuclide when \(_{19}^{40} \mathrm{K}\) decays via \(\beta^{-}\) decay.

Short Answer

Expert verified
Answer: \(_{20}^{40}\mathrm{Ca}\)

Step by step solution

01

Understand 尾鈦� decay process

In \(\beta^{-}\) decay, a neutron in a nucleus is converted into a proton, and an electron (called a beta particle) is emitted. As a result of this decay mode, the atomic number of the nucleus increases by one, but the mass number remains the same because the number of nucleons (protons + neutrons) in the nucleus is unchanged.
02

Determine the initial atomic number and mass number

The given nuclide, \(_{19}^{40} \mathrm{K}\), has an atomic number (Z) of 19 and a mass number (A) of 40.
03

Calculate the new atomic number and mass number after 尾鈦� decay

In 尾鈦� decay, the atomic number increases by one due to the conversion of a neutron into a proton, and the mass number remains the same. Therefore, after 尾鈦� decay, the new atomic number will be 19 + 1 = 20, and the mass number will still be 40.
04

Identify the daughter nuclide

The resulting daughter nuclide after 尾鈦� decay has an atomic number of 20 and a mass number of 40, which corresponds to the element calcium (Ca). Therefore, the daughter nuclide is \(_{20}^{40}\mathrm{Ca}\).

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Most popular questions from this chapter

In this problem, you will verify the statement (in Section 29.4) that the \(^{14} \mathrm{C}\) activity in a living sample is \(0.25 \mathrm{Bq}\) per gram of carbon. (a) What is the decay constant \(\lambda\) for \(^{14} \mathrm{C} ?\) (b) How many \(^{14} \mathrm{C}\) atoms are in \(1.00 \mathrm{g}\) of carbon? One mole of carbon atoms has a mass of \(12.011 \mathrm{g},\) and the relative abundance of \(^{14} \mathrm{C}\) is \(1.3 \times 10^{-12} .\) (c) Using your results from parts (a) and (b), calculate the \(^{14} \mathrm{C}\) activity per gram of carbon in a living sample.
(a) What is the mass defect of the 'H atom due to the binding energy of the electron (in the ground state)? (b) Should we worry about this mass defect when we calculate the mass of the \(^{1} \mathrm{H}\) nucleus by subtracting the mass of one electron from the mass of the \(^{1} \mathrm{H}\) atom?
The radioactive decay of \(^{238} \mathrm{U}\) produces \(\alpha\) particles with a kinetic energy of \(4.17 \mathrm{MeV} .\) (a) At what speed do these \(\alpha\) particles move? (b) Put yourself in the place of Rutherford and Geiger. You know that \(\alpha\) particles are positively charged (from the way they are deflected in a magnetic field). You want to measure the speed of the \(\alpha\) particles using a velocity selector. If your magnet produces a magnetic field of \(0.30 \mathrm{T},\) what strength electric field would allow the \(\alpha\) particles to pass through undeflected? (c) Now that you know the speed of the \(\alpha\) particles, you measure the radius of their trajectory in the same magnetic field (without the electric field) to determine their charge-to-mass ratio. Using the charge and mass of the \(\alpha\) particle, what would the radius be in a \(0.30-\mathrm{T}\) field? (d) Why can you determine only the charge-to-mass ratio \((q / m)\) by this experiment, but not the individual values of \(q\) and \(m ?\)
Calculate the activity of \(1.0 \mathrm{g}\) of radium- 226 in Ci.
What is the average binding energy per nucleon for ${ }_{11}^{23} \mathrm{Na} ?$
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