Hydrogen có ba đồng vị bền là 11H, 12H, 13H. Oxygen có ba đồng vị bền là 816O, 817O và 818O. Số phân tử nước có thể được tạo thành từ các đồng vị trên là
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Có 3 đồng vị Hydrogen: $^1_1H$, $^2_1H$, $^3_1H$.
Có 3 đồng vị Oxygen: $^{16}_8O$, $^{17}_8O$, $^{18}_8O$.
Một phân tử nước có 2 nguyên tử Hydrogen và 1 nguyên tử Oxygen.
Trường hợp 1: Hai nguyên tử H giống nhau: $H_2O$
Số cách chọn 2 nguyên tử H giống nhau là 3 ( $^{1}_1H_2O$, $^{2}_1H_2O$, $^{3}_1H_2O$ ).
Số cách chọn 1 nguyên tử O là 3 ( $^{16}_8O$, $^{17}_8O$, $^{18}_8O$).
Số phân tử nước tạo thành là: $3 imes 3 = 9$.
Trường hợp 2: Hai nguyên tử H khác nhau:
Số cách chọn 2 nguyên tử H khác nhau là $C^2_3 = \frac{3!}{2!(3-2)!} = \frac{3 imes 2}{2} = 3$ (ví dụ: $^1_1H$ và $^2_1H$).
Số cách chọn 1 nguyên tử O là 3.
Số phân tử nước tạo thành là: $3 imes 3 = 9$.
Tuy nhiên, vì thứ tự của các nguyên tử H không quan trọng, nên ta có $3 \times 3 = 9$ phân tử.
Tổng số phân tử nước có thể tạo thành là $9 + 3 = 12$.
Vậy đáp án là 12.
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