Question

1. apply: turn off show all and show neutron:proton ratio. predict whether the following isotopes will be stable. give a reason for each answer. check your answers in the gizmo. a. $_{8}^{20}o$ b. $_{20}^{40}ca$ c. $_{81}^{203}tl$ d. $_{92}^{238}u$

Explanation:

Step1: Determine number of protons and neutrons for $^{20}_8O$

Protons $p = 8$, neutrons $n=20 - 8=12$. Ratio $n/p=\frac{12}{8} = 1.5$. For light - elements (low atomic number), stable isotopes usually have $n/p\approx1$. This ratio is a bit high, and this isotope is unstable.

Step2: Determine number of protons and neutrons for $^{40}_{20}Ca$

Protons $p = 20$, neutrons $n = 40-20=20$. Ratio $n/p=\frac{20}{20}=1$. Calcium - 40 has a stable $n/p$ ratio and is a stable isotope.

Step3: Determine number of protons and neutrons for $^{203}_{81}Tl$

Protons $p = 81$, neutrons $n=203 - 81 = 122$. Ratio $n/p=\frac{122}{81}\approx1.51$. For heavier elements, stable isotopes have $n/p> 1$. But thallium - 203 has an odd - odd nucleus (odd number of protons and neutrons), and most odd - odd nuclei are unstable. So it is unstable.

Step4: Determine number of protons and neutrons for $^{238}_{92}U$

Protons $p = 92$, neutrons $n=238 - 92=146$. Ratio $n/p=\frac{146}{92}\approx1.59$. Uranium - 238 is a heavy element. Although it has a relatively high $n/p$ ratio, it is a long - lived radioactive isotope and is unstable as it undergoes alpha - decay over a long time.

Answer:

A. Unstable; High neutron - proton ratio for a light element.
B. Stable; Neutron - proton ratio of 1.
C. Unstable; Odd - odd nucleus.
D. Unstable; Undergoes radioactive decay (alpha - decay).