Listen Quran by radio or recorded, good work will be rewarded rights, no blame on him if he carries on business, or preoccupation, as long as heard as much as possible, and is either a job does not allow him to listen to the Quran, it should not because it goes against literature and respect.
Nawawi said in his book "Clarification of the Literature campaign of the Koran", Page 92:
ومما يعتنى به ويتأكد الأمر به احترام القرآن من أمور قد يتساهل فيها
بعض الغافلين القارئين مجتمعين . فمن ذلك : اجتناب الضحك واللغط والحديث
في خلال القراءة إلا كلاما يضطر إليه
And which should be paid attention to make sure it respected the Quran
from things that may leniency where some unsuspecting readers
combined. For example: avoid laughing and talking through reading
Quran only talk are forced him,
But complied with the words of God:
وَإِذَا قُرِئَ الْقُرْآنُ فَاسْتَمِعُوا لَهُ وَأَنصِتُوا لَعَلَّكُمْ
When the Qur'an is recited listen to it in silence. You may perhaps be
this reference in book "Fiqh on the four doctrines" "الفقه على المذاهب الأربعة" , Under paragraph: Terms of prostration of recitation "شروط سجدة التلاوة"
shows Shafi'i stated that it is not obligatory prostration (Sajdah) of recitation to who heard the Quran from not "Mokalaf" (human) Such as a machine recorder or radio, So the previous ayah ([7:204]) does not apply in the case of listening to the Quran from the recorder ...
This indicates there is no of sin on who was busy when heard Quran from recorder.