Question

Rutherfordium-257 was synthesized by bombarding Cf-249 with C-12. Write a nuclear equation for this reaction.

Answer 1

Answer:

• ²⁴⁹₉₈ Cf + ¹²₆ C → ²⁵⁷₁₀₄ Rf + 4 ¹₀n

Explanation:

Bombarding a nucleus of a heavy atom (high mass number) with other lighther nucleus is a kind of nuclear reaction named transmutation reaction: the elements become another kind of element.

1) General comments about isotopes:

The isotopes are specific type of atoms with a unique mass number. Different isotopes of an element have the same atomic number (number of protons) but different number of neutrons, which implies that different isosotpes of a given element have different mass numbers.

Mass number is the number of protons  and neutrons.

Denoting by Z the number of protons (or atomic number), N the number of neutrons, and A the mass number of the isotope,  you have this equation:

• A = Z + N.

2) Californium-249 (Cf-249)

Cf-249 is the isotope of californium with mass number 249.

Californium is the element 98 of the periodic table. That means that its atomic number is 98 (all the californium isotopes have the atomic number 98)

Hence, Z = 98, A = 249, and N = A - Z = 249 - 98 = 151.

Summarizing:

• Number of protons: 98

• Number of neutrons: 151

• Mass number: 249

The most convenient notation to use for isotopes, in order to complete a nuclear equation for the nuclear reaction, is using a superscript to the left of the chemical symbol for the mass number and a subscript to the right of the chemical symbol for the atomic number.

In this case: californium-249 = ²⁴⁹₉₈ Cf

3) Rutherfodium-257 (Rf-257)

Mass number: A = 257

Atomic number: Z = 104

Number of neutrons: N = A - Z = 257 - 104 = 153.

Summarizing:

• Number of protons: 104

• Number of neutrons: 153

• Mass number: 257

Notation: rutherfodioum-257 = ²⁵⁷₁₀₄ Rf

4) Carbon-12 (C-12)

Mass number: A = 12

Atomic number: Z = 6

Number of neutrons: N = A - Z = 12 - 6 = 6.

Summarizing:

• Number of protons: 6

• Number of neutrons: 6

• Mass number: 12

Notation: carbon-12 = ¹²₆ C

5) Nuclear equation:

• ²⁴⁹₉₈ Cf + ¹²₆ C → ²⁵⁷₁₀₄ Rf + 4 ¹₀n

This equation indicates that, when an atom of californium-249 is bombarded with an atom of carbon-12, one atom of rutherfodium -257 is synthesized along with 4 neutrons.

The symbol stands for the neutron particle, which has mass number 1 and atomic number 0 (no protons).

The law of conservation of the mass is observed on this equation when you check the balance on the number of protons and mass number on both sides of the equation:

                                        Left side                   Right side

• Mass number         249 + 12 = 261          257 + 4(1) = 261

• protons                   98 + 6 = 104              104 + 4(0) = 104