Answer:
Let \[{{N}_{1}}\] and \[{{N}_{2}}\] be the number of undecayed nuclei present at times \[{{t}_{1}}\] and \[{{t}_{2}}\] respectively. Then \[{{R}_{1}}=\left| \frac{d{{N}_{1}}}{dt} \right|=\lambda {{N}_{1}}\] and \[{{R}_{2}}=\left| \frac{d{{N}_{2}}}{dt} \right|=\lambda {{N}_{2}}\] \[\therefore \] \[{{R}_{1}}-{{R}_{2}}=\lambda ({{N}_{1}}-{{N}_{2}})\] or \[{{N}_{1}}-{{N}_{2}}=\frac{{{R}_{1}}-{{R}_{2}}}{\lambda }\] Clearly, \[({{N}_{1}}-{{N}_{2}})\]is the number of nuclei that have disintegrated in time interval \[({{t}_{1}}-{{t}_{2}})\].
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