{"id":22571,"date":"2020-07-25T14:15:39","date_gmt":"2020-07-25T13:15:39","guid":{"rendered":"https:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=22571"},"modified":"2020-07-25T14:15:39","modified_gmt":"2020-07-25T13:15:39","slug":"question-for-the-day-einstein-special-relativity-and-atomic-weights","status":"publish","type":"post","link":"https:\/\/www.rzepa.net\/blog\/?p=22571","title":{"rendered":"Question for the day – Einstein, special relativity and atomic weights."},"content":{"rendered":"
\n

Sometimes a (scientific) thought just pops into one’s mind. Most are probably best not shared with anyone, but since its the summer silly season, I thought I might with this one.<\/p>\n

Famously, according to Einstein, m \u00a0= E\/c^^2, the equivalence of energy to mass. Consider a typical exoenergic chemical reaction:<\/p>\n

\u00a0A \u2192 B, \u0394G -100 kJ\/mol. \u00a0<\/p>\n

According to the above, the molecule looses 100 kJ\u00a0\u2261 1.112650056053618e-18 g after transformation from A to \u00a0B. Not much, but possibly measurable using today’s very best technology.<\/p>\n

Now for the questions that might arise.<\/p>\n

    \n
  1. What sort of energy applies above? \u00a0If its a free energy, then thermal (zero point and entropic vibrational) energy must clearly contribute. Or is it total energy without thermal and entropic contributions?\u00a0<\/li>\n
  2. Is the mass loss distributed equally amongst all the atoms. In other words, how much mass does any particular atom lose after reaction or is this question meaningless?<\/li>\n
  3. Since clearly the atoms must each lose some mass, that must mean that their atomic weight is a function of the energy content of the molecule they are part of. \u00a0A molecule with a lot of internal energy (lets say octanitrocubane, which decomposes to carbon dioxide and nitrogen) must have heavier atoms in the form of cubane than as nitrogen gas.<\/li>\n
  4. And to recapitulate the question above, how many orders of magnitude away (if any) might we be from being able to measure this? Or, one can repose this question by asking whether one can measure the mass lost by a battery after discharging?<\/li>\n<\/ol>\n

    As with most spontaneous questions, the answers are probably all out there somewhere. Just a matter of finding them!<\/p>\n

    \n

    Here is a real-world example. At the large hadron collider at CERN, about 1011\u00a0<\/sup>protons are accelerated to almost the speed of light. During this process, they acquire a mass approaching kgs (I do not recollect the exact value). It certainly is a surprisingly large mass! And it is a surprisingly large amount of energy that has to be injected to achieve this. And when the beam is quenched, that mass is very quickly lost (and a lot of heat is generated in the quenching tunnel).<\/p>\n\n<\/div> ","protected":false},"excerpt":{"rendered":"

    Sometimes a (scientific) thought just pops into one’s mind. Most are probably best not shared with anyone, but since its the summer silly season, I thought I might with this one. Famously, according to Einstein, m \u00a0= E\/c^^2, the equivalence of energy to mass. Consider a typical exoenergic chemical reaction: \u00a0A \u2192 B, \u0394G -100 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[4,6],"tags":[1524,1526],"class_list":["post-22571","post","type-post","status-publish","format-standard","hentry","category-general","category-interesting-chemistry","tag-general","tag-interesting-chemistry"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p1gPyz-5S3","jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=\/wp\/v2\/posts\/22571","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=22571"}],"version-history":[{"count":0,"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=\/wp\/v2\/posts\/22571\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=22571"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=22571"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.rzepa.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=22571"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}