Trong tự nhiên, magnesium có 3 đồng vị bền là 24Mg, 25Mg và 26Mg. Phương pháp phổ khối lượng xác nhận đồng vị 26Mg chiếm tỉ lệ phần trăm số nguyên tử là 11%. Biết rằng nguyên tử khối trung bình của Mg là 24,32. Tính % số nguyên tử của đồng vị 24Mg và 25Mg.
1. % 24Mg = %.
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Ta có hệ phương trình:
- $x + y + 11 = 100$ (Tổng % các đồng vị bằng 100%)
- $24x + 25y + 26*11 = 24.32*100$ (Nguyên tử khối trung bình)
Giải hệ phương trình:
- $x + y = 89$
- $24x + 25y = 2432 - 286 = 2146$
Nhân phương trình thứ nhất với 24: $24x + 24y = 24*89 = 2136$
Lấy phương trình thứ hai trừ phương trình vừa tạo: $y = 2146 - 2136 = 10$
Vậy % 25Mg = 10%
Suy ra $x = 89 - 10 = 79$
Vậy % 24Mg = 79%
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