Question

which statement correctly identifies the nuclide that is most likely to be unstable and describes why? uranium-238 (²³⁸u) is likely an unstable nuclide because it has a neutron - to - proton ratio that is 1.6:1 and the ideal neutron - to - proton ratio is 1:1. uranium-238 (²³⁸u) is likely an unstable nuclide because it has a neutron - to - proton ratio that is 1.6:1 and the ideal neutron - to - proton ratio is 1:2. carbon-14 (¹⁴c) is likely an unstable nuclide because it has 8 neutrons and 6 protons, and the ideal neutron - to - proton ratio is 1:2. carbon-14 (¹⁴c) is likely an unstable nuclide because it has 8 neutrons and 6 protons, and the ideal neutron - to - proton ratio is 1:5.

Explanation:

Step1: Recall stability - neutron - proton ratio

For light - elements, the ideal neutron - to - proton ratio is close to 1:1. For heavier elements, the ideal neutron - to - proton ratio is greater than 1:1.

Step2: Analyze Uranium - 238

Uranium - 238 ($^{238}$U) has atomic number $Z = 92$ (number of protons) and mass number $A=238$. The number of neutrons $N=A - Z=238 - 92 = 146$. The neutron - to - proton ratio is $\frac{N}{Z}=\frac{146}{92}\approx1.6:1$. For heavy elements like uranium, a neutron - to - proton ratio greater than 1:1 is expected. But it is still unstable due to its large size and complex nuclear structure.

Step3: Analyze Carbon - 14

Carbon - 14 ($^{14}$C) has atomic number $Z = 6$ (number of protons) and mass number $A = 14$. The number of neutrons $N=A - Z=14 - 6 = 8$. The neutron - to - proton ratio is $\frac{N}{Z}=\frac{8}{6}=\frac{4}{3}\approx1.33:1$. For light elements like carbon, the ideal neutron - to - proton ratio is close to 1:1. Carbon - 14 is unstable because its neutron - to - proton ratio is not close enough to 1:1.

Step4: Evaluate options

The ideal neutron - to - proton ratio for light elements is close to 1:1. Options with ideal ratios of 1:2 and 1:5 are incorrect. Uranium - 238 is unstable because its neutron - to - proton ratio of 1.6:1 is not in the most stable range for its mass, and the ideal neutron - to - proton ratio for light elements is 1:1, not applicable for heavy - elements like uranium.

Answer:

Uranium-238 ($^{238}$U) is likely an unstable nuclide because it has a neutron - to - proton ratio that is 1.6:1 and for light elements the ideal neutron - to - proton ratio is 1:1. (Note: The correct statement about uranium - 238 should mention that for heavy elements, the ideal ratio is greater than 1:1 but 1.6:1 is not in the most stable range for uranium, and the reference to 1:1 in the option is likely a mis - statement about the general concept of stability and neutron - proton ratio. However, among the given options, this is the most correct one in terms of the general idea of neutron - proton ratio and nuclear stability).