List of top Geology and Geophysics Questions on Radioactive Decay asked in GATE GG

230Th and 226Ra are intermediate nuclides in the decay series of 238U to 206Pb. The half-lives of 238U, 230Th, and 226Ra are 4.47 billion years, 75,000 years, and 1600 years, respectively. At secular equilibrium, when activities are equal, 10 billion atoms of 238U are present. The number of atoms of 226Ra present at equilibrium is ________
230Th and 226Ra are intermediate nuclides in the decay series of 238U to 206Pb. The half-lives of 238U, 230Th, and 226Ra are 4.47 billion years, 75,000 years, and 1600 years, respectively. At secular equilibrium, when activities are equal, 10 billion atoms of 238U are present. The number of atoms of 226Ra present at equilibrium is ________
The decay constant of a radioactive isotope is \(1.21\times 10^{-4}\ \text{year}^{-1}\). The half-life of the isotope is $\underline{\hspace{3cm}}$ years. [round off to nearest integer]
The heat production (\(Q_r\)) of a granitic rock due to decay of the radioactive elements U, Th and K having concentration \(C_U, C_{Th}, C_K\), respectively, is given by the expression: \[ Q_r = \alpha C_U + \beta C_{Th} + \gamma C_K \] Which one of the following correctly represents the relation between the magnitude of coefficients \(\alpha, \beta, \gamma\) (in \(\mu Wkg^{-1}\))?
The following reaction occurs at 1 bar and 823 K. Grossular + Quartz = Anorthite + 2 Wollastonite
Using the above molar thermodynamic data, the calculated slope of the above reaction is ________ bar K\(^{-1}\). [round off to 2 decimal places]