test","extracted_subject":"PHYSICS","extracted_chapter":"NUCLEI","extracted_topic":"RADIOACTIVITY","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_848.png?top_left_x=0&top_left_y=1418&width=532&height=270&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23c9b70136192204c0acf","slug":"a-and-b-are-two-radioactive-substances-whose-half-","content":"A and B are two radioactive substances whose half lives are 1 and 2 years respectively. Initially 10 gm of A and 1 gm of B is taken. The time (approximate) after which they will have same quantity remaining is –","options":[{"_id":"68a405ef7f15af4716c8a52a","text":"6.62 years","sequence":0,"isCorrect":true},{"_id":"68a405ef7f15af4716c8a52b","text":"5 years","sequence":1,"isCorrect":false},{"_id":"68a405ef7f15af4716c8a52c","text":"3.2 years","sequence":2,"isCorrect":false},{"_id":"68a405ef7f15af4716c8a52d","text":"7 years","sequence":3,"isCorrect":false}],"correct_answer":"6.62 years","explanation":"M_A= M_B Ž \\(\\frac { 10 } { 2 ^ { t / 1 } }\\) = \\(\\frac { 1 } { 2 ^ { t / 2 } }\\) Ž 2^t/2 = 10\n\nlog₁₀ 2 ^t/2 = log₁₀ 10 Ž \\(\\frac { \\mathrm { t } } { 2 }\\) log₁₀ 2 = 1\n\nt = \\(\\frac { 2 } { \\log _ { 10 } 2 }\\) = 6.62 years","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:41:47.891Z","__v":0,"vector_store_id":"8bf008f6-6ff6-4c01-931a-5a2a3675c451","updated_at":"2024-08-30T21:41:47.891Z","isStarred":false},"params":{"questionSlug":"a-and-b-are-two-radioactive-substances-whose-half-"}}]}]]

Question: A and B are two radioactive substances whose half lives are 1 and 2 years respectively. Initially 10...

Solution