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Hint-The actinium series in the periodic table is a radioactive series that means all the elements of this series are radioactive. Actinium series is a $4n + 3$series, Hence this shows that when the mass number is divided by four $4$ then remainder will be $3$.

On checking each option given in the question, we see that,

For option (A) mass number =$235 = 4 \times (58) + 3$

So, the remainder is $3$.

For the option (B) mass number=$232 = 4 \times (58) + 0$

So, the remainder is $0$.

For the option (C) mass number =$225 = 4 \times (56) + 1$

So, the remainder is$1$.

For the option (D) mass number=$34 = 4 \times 8 + 2$

So, the remainder is$2$.

For the option (E) mass number=$217 = 4 \times (54) + 1$

So, the remainder is$1$.

So here we see that the only mass number is $235$which gives the remainder \[3\] on dividing it with $4$. Hence the only \[{}_{92}{U^{235}}\;\]is the member of the actinium series among the all five given options.

So, option (A) is the correct answer.

Note-Actinide series contains the atomic number from 89 to 103. Some properties of the actinium series are as follows-

1- known as rare earth metals.

2- Since they are unstable in nature that’s why they are radioactive metals.

3- Majority synthetically made by the particle accelerators creating nuclear reactions and making them short lasting or unstable. That’s why they have the ability to undergo nuclear reaction.

4- All elements of actinides have the ability to make stable complexes with ligands, such as chloride, sulphur, carbonate and acetate.

5- Many of the actinides are found in nature as sea water or minerals.

6- Actinides when they are radioactive form then on interaction with different types of phosphorus will produce a pulse of light.

__Complete step by step solution:__On checking each option given in the question, we see that,

For option (A) mass number =$235 = 4 \times (58) + 3$

So, the remainder is $3$.

For the option (B) mass number=$232 = 4 \times (58) + 0$

So, the remainder is $0$.

For the option (C) mass number =$225 = 4 \times (56) + 1$

So, the remainder is$1$.

For the option (D) mass number=$34 = 4 \times 8 + 2$

So, the remainder is$2$.

For the option (E) mass number=$217 = 4 \times (54) + 1$

So, the remainder is$1$.

So here we see that the only mass number is $235$which gives the remainder \[3\] on dividing it with $4$. Hence the only \[{}_{92}{U^{235}}\;\]is the member of the actinium series among the all five given options.

So, option (A) is the correct answer.

Note-Actinide series contains the atomic number from 89 to 103. Some properties of the actinium series are as follows-

1- known as rare earth metals.

2- Since they are unstable in nature that’s why they are radioactive metals.

3- Majority synthetically made by the particle accelerators creating nuclear reactions and making them short lasting or unstable. That’s why they have the ability to undergo nuclear reaction.

4- All elements of actinides have the ability to make stable complexes with ligands, such as chloride, sulphur, carbonate and acetate.

5- Many of the actinides are found in nature as sea water or minerals.

6- Actinides when they are radioactive form then on interaction with different types of phosphorus will produce a pulse of light.

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